Organic Group own manu

I have setup Organic Groups.
Is there a way for each group to have their own menu?
Or when you look at a group you only see the menu posts relating to that group.

The group manager should only be able to create/edit his own group menu posts.

If there is a group "fungroup" the manager creates a content post and add it to the menu "groupsmenu".
When a user visitis the "fungroup" there is the menupost in the menu "groupsmenu".
However, when a user visits "othergroup" there is nothing in "groupsmenu".

Do I make sense?
Is there a module that does this?

Thanks