If you create a group, you are the group owner.
Group owner: has control over membership, discussions, settings, subgroups, rules and more. They can also transfer ownership of a group to another group manager.
Group manager: has the same access to the group as the owner except they can't close or transfer ownership of the group.
Group moderator: limited to monitoring discussions and comments and managing submission and moderation queues. They can also feature a discussion.
All three roles can: