I had earlier about linking a part of the general forums to groups, but apparently that's not possible. Someone replied about giving groups a forum functionality of their own (that post is now deleted for some reason), but I wasn't able to get that to work. I found out why that did not work and would like to report that.
If you create a group, then go to forum plugins and give groups a forum funtionality and go check your previously created forum it does not show the forum under the group. However, if you now create a new group it will have the forums properly.
If that is a feature you might want to clarify the order of creating things (forums for groups first, then group creation).