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.