Seeing how
CD47-Bot hasn't been seen too often around these parts lately...
Could the creation of groups be modded to allow any user* to create a group and have anyone be able to join said group, much like how Facebook works? (Unless it was an invite-only group.) To avoid problems, would need the approval of a moderator before they could be created. In addition to this, while ordinary members could become "Officers" of the group, each group would also need at least one moderator to "Officer" as well.
And if we really want to get cool, you can have certain tags from CD-Media/CD-Events be "connected" to certain groups. Such as if there were New England FIRST or IndianaFIRST groups, then tags such as "UTC Connecticut Regional" or "IRI" could be associated to their respective group. On their specific group page, all pictures with the tags associated to that group could be shown, just as in CD-Media.
* Well, we could put something there there like you need at least 10 posts and/or 100 rep points, so spam posters can't create bogus groups.