When trying to display a list of subspaces of a current space, I also see "No permission" spaces and their subspaces.
The displaying of "No Permission" is a known issue. We are tracking it in this ticket:
Getting issue details...STATUS
It seems, that if you grant access to single users, the "No Permission" disappears, but as soon as you use groups to restrict the space, it will appear for users without the proper rights. This might explain, why you see only several "No Permission" spaces.