When I go to "site permissions" I can see groups that have some permissions and modify their permissions level, but groups without any permissions set do not appear in the list. I can see them in "People and groups" but even if I edit their properties I don't see a way to add permissions. I can delete them and recreate them with permissions, but there has to be a way to just add permissions to a group without any right?
I am assuming that you are setting permissions for a subsite that has chosen not to inherit permissions from the parent site. In which case, merely go to the permissions for the subsite and Add the group that you want to have access to the site and then grant it the permission that you want for the site.