Within every group there are four types of users, listed in order of least to most privileged: members, moderators, administrators (admin), and owners.
Members of a group may browse the group and interact with its posts, chat, and users.
Moderators inherit all Member privileges, plus the ability to accept or reject posts upon post submission, the ability to ban/invite users, and pin/unpin posts, and the ability to remove posts.
Admin inherit all Moderator privileges, plus the ability to change the group's settings and grant/remove admin/moderator privileges to another user.
Owners inherit all Admin privileges plus the ability to delete the group.