I don't have any data at hand, but here's my feeling based on what I've seen on the site and a few things to keep in mind for this topic.
You can't see who voted to close before the closing is complete, so long as people don't explicitly comment.
If I see a question in the review queue and no comments indicating any problems I often leave a Reminder to Close-Voters to prompt others to state what they think is wrong with the question. Other people do this regularly, too, if there hasn't been any comment. So the second or third person to get a close vote in the review queue can often see at least one person who said something that may be wrong with a question.
But still: you normally don't know who voted to close until the question is put on hold. Just like you can't normally see who voted to reopen until the question is reopened.
You could go to your review history after casting your vote and see who voted for what, but that's already after the fact.
This makes it hard for cliques to know when their voting-buddy voted for something.
There is no private messaging integrated into the SE network.
Nobody can send a private message to someone indicating something like "Hey, how about we close this question?" inside of the normal network.
It would require the participants to get acquainted outside of the network, which increases the amount of work slightly that would be required, just for this kind of action.
The closest you can get inside of the normal SE network is the chat, which everybody can access to write who has at least 20 reputation. And everybody can read it, no matter the reputation. This is a very low mark and there are no other requirements to be part of this "clique". In fact we would love if more people regularly visited the chat to talk about their ideas/projects/... I've seen it sometimes (maybe once a month or every two months?) that someone posts a blatantly off-topic question there to start a discussion with the regulars who are online at the moment. Or about a question that needs reopening, because the author edited his question. Or about asking people to help with editing to give a new user some hints. A lot of the regulars in the chat have enough reputation to vote for close/reopen/edit/..., which makes this the ideal place to talk about pro and con of putting something on hold.
There was even a special chat room for talking about reopening.
Bottom line: the chat may be somewhat active at times, but there is not even enough attention to maintain a chatroom for this topic. The special room was frozen and it's very rare that a question pops up in the chat for VTC/VTO. And the discussions tend to be quite diverse. The people there are not thinking "Ah, I know that username, so the question he mentioned must be closed immediately." - we openly talk about why a question should be put on hold or reopened if the case arises. Still, you could call it a "clique" if you wanted to. It's the closest thing you can get to a "clique" on this site anyway as the amount of regular chat users is quite limited, although everyone with a very little amount of 20 reputation can be part of this very open "clique".
There are Meta discussions.
More often than in the chat someone posts something about closing/reopening on Meta. This leads to the regular Meta users seeing the question and acting on them, as a lot of them also have higher rep. Again, this could be seen as a "clique", even if it's open to everyone. It's commonly referred to as the Meta Effect. But these Meta discussions are still not something that leads to people thinking "Ah, yes, gotta close". They are open discussions where different people offer different views.
People can post on Meta with 5 reputation. Again, reading is possible even for people that are not logged in to the site. It's open for everyone. And 5 reputation is a single answer or question upvote. It's a tenth of the reputation you need to be able to comment everywhere. This could be seen as a "clique", but just like the chat, it's a very open and welcoming "clique". More activity on Meta would also be a great thing. There can't be too many people active in the chat / on Meta, so getting more opinions about how closing/reopening/... should work on the site would be great and people listen to arguments - not to the username that posted something.
Regular close voters often have somewhat similar patterns.
I know that there are a handful of people that very often vote similar to how I am voting. Seeing their username in the comments does in fact draw my personal attention because I know how they comment and realized through experience that they are very good at filtering the noise or summarizing problems/possible solutions. Data would surely suggest that we are a "clique" - mainly because they just vote similar most of the time.
Just because people vote similar doesn't mean they stop thinking the moment one of them posts something. For example those people I have in mind have a similar opinion most of the time - just not when it comes to questions tagged magic. There are surely similarities in the voting pattern, but also bigger differences.
A question that is put on hold without any real reason can easily be reopened.
Posting on Meta and asking for the reasons for a question that was put on hold will draw in people that look at the question and you will surely find people that see the merit. If there are enough the question can be reopened. And as you can only VTC once on every question there won't be a war. You may see patterns of people who don't like magic questions for example voting to clsoe these questions and people who like them and vote to reopen - in the end the whole active community decides.
People show dramatically different levels of activity when it comes to reviewing.
Some people review a lot. Some people don't like reviewing at all.
You will surely find that a few people VTC very often, especially compared with the average user. You could say that they are a "clique". It would probably look like it. But someone has to do the reviewing if we want high quality questions and answers on the site. If you feel there are too few reopen votes for example the best thing to do is to lead with a good example by raising the topic on Meta/in chat regularly and trying to focus on the reopen review queue. But just like you might want to focus on the reopen queue you will find people who focus on the closing queue. Because that's also an important part of the community.
I don't think there are "cliques" of people on this site. Yes, there are some people who are more strict/lenient when it comes to certain topics and there are groups that you will find more often as reviewers, such as regular Meta users and regular chat users, but it's not like they are always voting for the same thing or stop to think once they see someone vote. And there are no groups who regularly invite others to close a bunch of questions they don't like. This would probably have the adverse effect quite often - if you can't say why you want to close something I for example tend to give the querent the benefit of doubt.
But I am sure that any data would reveal that some people are very often co-voting. I can think of a few people that I would expect to see with a similar voting pattern to mine because we have a similar take on a lot of topics. Participating in a lot of discussions about these topics, because we always had them and will always have them on this site, leads to that, which is also a good sign that there are certain rules that people can follow to know whether something is on-topic or off-topic.