His son, Ogedai Khan, expanded the empire even more. And Genghis's grandson, Mongke, was the Great Khan in 1258 when Baghdad, the capital of the Abbasid Empire, fell to the Mongols. And another of Genghis's grandsons, Kublai Khan, conquered the Song Dynasty in China in 1279. And if the Mamluks hadn't stopped another of Genghis's grandsons at the Battle of Ain Jalut, they probably would have taken all of North Africa. Man, Genghis Khan sure had a lot of grandkids. Well, it must be time for the open letter. An Open Letter to Genghis Khan's Descendants.