By default  when you create  a new site  the Visitors, Members, and Owners group
you get is the one from the Site collection  Level. You don't get a Site
specific set of groups  unless you Break Inheritance. If you create an
Approver's group  at the Top Level Site of the Site Collection it will be
inherited by all Sites by default. If you want to break Inheritence by default
and create a Site Specific group you would need to do this in Custom code.

So when I create  a subsite, and I get the option to create permission  groups or
inherit permissions, if I choose to create new groups, I can create 3 new
permission groups  for that subsite. I know that I can create a group  in the
"people" settings, but there is no way to add  more "default" groups on the page
where groups are set up? I figured I would have to dive into the code on the
"permsetup.aspx" page  to accomplish  what I was looking for, I just wanted  to
make it a little more convenient to manage the "approvers" group when the sub
site was created. As it is right now, when I create a subsite, I set up the 3
default groups and then I have to do a complete song and dance just about to get
an approvers group set up at the site  level. I don't want to split everything
out into multiple  site collections because of the way that our site is accessed
internally and externally, and because there is actually quite a bit of
interaction between the
different sites, with some automation that I have built in using SPD.
(Approved documents get copied to a different document library on a different
subsite with a different set of permissions, and all of this happens as a
precursor to being "published" officially.) Moving subsites  into top level
sites and site collections, although not be impossible, will be very difficult
and very administrator (me) intensive. If it can't be done, then so be it, and
I will continue manually creating  the "approvers" groups. I just wanted to save
myself a few steps if at all possible. (One of the difficulties is that each
site will have a completely different set of approvers.)

That actual prompt when you create  a new site  is to inherit permissions or
create Unique permissions. As I said there is no way to create another default
group that would be part of the unique permissions other than custom code. In
general in SharePoint there is no code on a page, so diving into code on the
permsetup.aspx page  won't help. You would have to re-write the managed code
assembly behind that page. There is no easy way to do what you are trying to
do.