To delete a group, all you need to do is click on People then on Groups. Next, click on the group that you want to delete.
In the next page, click on the Settings tab and click on Delete.
That's it! If you had any subgroups, those groups would move up in the ladder. If you look in the first image, you'll see that the group that was deleted had two subgroups. After deleting the group, the two subgroups moved up one level, shown with circles.