To delete a group, you first have to remove all its members and then leave it. If you leave the group without previously removing all its members, the group will remain there and you will lose your admin status, so you won't be able to delete this group anymore.

To remove all member first go to group you want to delete, then Click "see all" or click members area htne remove all the members of the group, last to remove is your self, the admin.

The Facebook will show you a message telling you that, since you are the last member, leaving the group will also delete it. Just click on the “Delete Group” button to confirm the action.