The minimum spread between the front and back holders (clamps) has to be 44 inches on centers. I already know that Thule and Yakima do not make one that fits the QX56.
I have used the Yakima Skybox 18 Pro on my 04 QX56. The local dealer was unable to help me and sent me to a roof rack supply house. They said this was the only one that would fit and it is not a perfect fit but seems to do what I need.