How do I control the CSS that the groups inherit from the overall system-wide setting?
CSS Code Customizations
You can set each group to inherit all, some, or none of the custom CSS code from the System-wide Look & Feel Settings. This includes the Custom JS/CSS Code, Custom Header Code, and Custom Footer Code boxes.
Admin Stuff > Groups > Group Settings icon > Group Look & Feel tab
1. System Code Customizations
Each Group Customization page has its own Custom Head, Header, and Footer boxes for any style changes or other customizations you'd like to have for that group.
You must uncheck the "Code Inherit" box if you don't want that group to inherit the system-wide customizations in addition to whatever you add on the group customization page. If you do not, it will continue to inherit the custom code from the System-wide Settings page in addition to anything you add on the Group Customization page.
2. Group Code Customizations