Create a menu with a list of all groups
I am not clear what is your requirement. If you want to create a single menu page and want to show list of group name , you can do this using views. Create a view page and list your content and select menu type as normal nemu item.

OR

If you want to create list of menu items according to group name, in that case you should try to create custom menu using hook_menu.
check here https://api.drupal.org/api/drupal/modules%21system%21system.api.php/function/hook_menu/7