Yes, you can! Groups and Courses in your Mighty Network can have their own privacy settings, their own features, their own posts and events, their own Topics, and their own custom logo and theme color.
Group Privacy Settings
A Public Group or Course is visible to both members and visitors, and anyone can join.
Private Groups and Courses are listed in your Mighty Network, but only invited members or members that request to join and are approved can see the activity inside.
A Secret Group or Course is hidden from everyone except invited members and Network Hosts.
If you want to update the privacy settings on a Group or Course later, you can do so anytime by going directly to your Group or Course, navigating to Settings, and selecting General Settings.