The MoveGroup method moves a group from one containing group to another. This method can also be used to change the position of a group within the containing group.
void MoveGroup( long groupId, long destGroupId, int index )
The groups identified by the groupId and destGroupId parameters must be owned by the currently authenticated user.
To change the position of a group within its current containing group, specify the identifier of the containing group in destGroupId. The index parameter is zero-based, that is, the very first item in the group has index 0, the following item has index 1, and so on.