Organization owners are the only ones who can create new groups, by default. An organization owner can allow members of the team group to create private groups. Only owners can create public groups.
Note: the team group generally isn't named "team". Any previously existing group can be designated as the team group.
If an organization has public groups, a group admin can choose whether the public can join a group, see the posts (but not join it) and whether the group member list is visible.