Here's a handy guide to creating different user roles for your Google Groups.
More details are here > https://support.google.com/groups/answer/2464975?hl=en
1. Login to admin.google.com/yourdomain.com
2, Select "Groups"
3. Select the Group you want to manage
4. Select "Access Settings"
5. On the left you should see a "Roles" link
6. From here you can edit your existing roles (typically Owner, Manager and Member) or CREATE A NEW ONE to go fully custom. You can create many additional roles. For the default roles, an Owner has full permission, a Manager can do everything but delete the group or make themselves the Owner, and a Member is a regular user. You can customize those existing default roles as needed by checking the box and editing Permissions there.
7. If you CREATE A NEW ROLE, add some details about it.
7. Then Add/Edit the Permissions for that Role, Save and You're All Set!