40 years of SNL and No Genesis

I watched the Saturday Night Live this Sunday and enjoyed the music played throughout the show. While watching the portion of the show that was dedicated to the 40 years of music, I began to wonder why Genesis never appeared on SNL. Especially during the early years. Other British groups and solo acts appeared throughout the years. Why not Genesis. It could be as simple as the schedules never matched or both parties never connected. However, I cant help but wonder how cool a Genesis appearance would have been for the group. After all, they appeared on Mike Douglas, why not SNL