I reviewed some of the admin files and was able to extract what is needed to be able to add in group types for the group creation process.
This is for the GroupsAdd.ascx template and is a manual process. Meaning that you will have to manually add in all group types into the template using asp:ListItem for all your group types. Also note: if you add any other new group types through the admin CP, you will also want to add the new option to your template. This should also work for the groupsedit template, but I have not tested it yet.
<asp:DropDownList ID="drpGrpTypes" runat="server">
<asp:ListItem Value="0">[RESX:NotSpecified]asp:ListItem>
<asp:ListItem Value="1">Group Type 1asp:ListItem>
<asp:ListItem Value="2">Group Type 2asp:ListItem>
<asp:ListItem Value="3">Group Type 3asp:ListItem>
asp:DropDownList>
I tested this with Admin and a regular user. Also went back into the admin cp and verified after group creation, the group has the correctly assigned group type.
Note: This is not a supported by AM and use at your own risk.
Edit: FYI: I just tried testing with setting a default value by using the "selected="true" and "selected="selected" value, and this does not work.