Allow users to request membership of groups

It would be great if users with specific classifications (ie., our internal users) could see all groups within that specific classification with the ability to "request to join" a group. Ie., a new music teacher would sign in and when they go to place a request, see all school departments including music, and "request to join". This would alleviate the need for dept. heads to remember to add all users to their groups at the start of each year.