Make the game public

Open your centre (game) in the Roblox Studio.

Open "Game Settings".



Go to "Permissions" at the left side of the screen that popped up.



Set it to "Public" and press "Save".



Show public games at your group

This can only be configured by the owner of a group.

Navigate to your group page, like this:



Click on the 3 dots at the upper right side of your screen and select "Configure Group"



Navigate to your group settings at the left sidebar.



Switch the setting "Group games are visible on the group home page" on.