Add/manage private group

I have a question about private group :
It is possible to create a private group via a user other than admin ?

My user must be able to manage a private groupe (create/edit, add users, etc…).
I have to add some trust levels ?

Thanks for your help

AFAIK, only Admins can create Groups, but you can assign a Group Owner who can then manage that group (add/remove users from the group)