Removing menu from group?

Hello... first post and request - as I'm stuck! I'm used to extensive searching for solutions but not found one to this:

I'm familiar with how to remove a group from the menu - but not the reverse - meaning removing the menu from a group. Essentially I want some groups (not all) to have no menu (and maybe no top bar) so that people (defined as guests) accessing a group (effectively a page on a browser) can then not find other groups/pages.

Is this possible?