As a group admin, I get requests from people from various organizational accounts, many of whom wish to keep their profiles "hidden" (i.e. not public). However, I need to see a person's info in order to determine if they can join our group. Also, members within our group need to see each other's information.
In the Profile Edit page, under the "Who can see your profile?" it would be great to have a fourth option that read "Group Members and Groups you are requesting to join".