You can hide the entire people menu from students in course settings but hiding a group isn't possible that I know of. There is a setting for not allowing student created groups.
We are giving the Canvas Admins area a little bit of love and just want to check in with you. This will also bring this question new attention.
Were you able to find an answer to your question? I am going to go ahead and mark this question as answered because there hasn't been any more activity in a while so I assume that you have the information that you need. If you still have a question about this or if you have information that you would like to share with the community, by all means, please do come back and leave a comment. Also, if this question has been answered by one of the previous replies, please feel free to mark that answer as correct.
I have a similar question in that we need to have our customer service people (and other test accounts) enrolled in courses so they can see what students are seeing. I would like to keep those people/accounts hidden from the students, though, so students don't contact those people/accounts through the course. We want students to use the Help methods we set out.
We are currently asking ourselves the same question for our class.
The Groups function is highly desirable, and I want students to be able to create their own groups and sign up for them, this is all good. But it appears that this is impossible without making all 1200 students in the class visible to each other by enabling "People", which we currently hide.