I see groups like a subscriptions to categories, therefore I think it would be cool to have a "frontend groups manager" to have all groups listed with checkboxes, so users can join and leave PUBLIC groups easily.
Check or uncheck and save.
Private and hidden groups could be excluded since you need to ask for membership and hidden are hidden.
This would be very helpful for users being a member in a lot of public groups.
It a very useful tool on many blogs with subscriptions to categories.