When a group is deleted, users will lose the group permissions and equipment permissions granted to the group. If specific group or equipment permissions are granted to users through another group, they will still be able to retain the permission.
Be careful when removing groups with the Manage Groups permission. If all users lose the Manage Groups permission, there will not be any users who will be able to mange your groups. Contact Boathouse Connect if this happens to re-add the permission to at least one group.