How do I create subgroups within my GROU.PS network?
You can do this by activating the Groups module in your group. For a quick guide on how to do this, check out: http://www.groups-corp.com/wiki/item/using-the-subgroups-module
How can I prevent members from creating subgroups?
You can change this option by going to the management page of your subgroups module
Select the Admins only option for "Who can edit the content?" of subgroups. This will prevent members from creating additional subgroups.