Groups don't have parents. The comoposition relationship does not represent a hierarchy in that way.
To solve the problem you are referring to I subtyped the group object with my own object type to represent the hierachy of a company. The table for these company groups did include a parent_id column to represent the hierachy. When I created these groups I set the context_id to be the whatever group was set as the parent_id.
This was used to assign who had permission to add and remove members from a group in this case and to see details of am employee.
