Map<Group, Map<Username, GroupMember>> groups

public class Foo {

    private final Map<Group, Map<Username, GroupMember>> groups;

    //...

    public void addGroup(Group group) {
            if (exists(group))
                throw new IllegalOperationException("Group with same name already exists");
            //Declaring a new HashMap within the class (i.e. defining the implementation within a class member)
            groups.put(group, new HashMap<Username, GroupMember>(Map evaluation based on group object)));
    }

    //...
}

//Passing Map<Username, GroupMember> object decreases abstraction and exposes implementation details
public void addGroup(Group group, Map<Username, GroupMember> groupMembers) {
        if (exists(group))
            throw new IllegalOperationException("Group with same name already exists");
        groups.put(group, groupMembers));
}

public class Group {

    private final String name;
    private final String description;
    private final Instant dateCreated;
    private final Collection<GroupMember> members;

    //... Constructor and getters for the fields
}