Which empire defeated Babylon and came next in Daniel 2?

Les explains that in Daniel 2, the head of gold was Babylon, a government of one absolute dictator who did not have to consult anyone. The next kingdom that came on the scene and defeated Babylon was the Mede and Persian Empire. Militarily they were already greater than Babylon, otherwise they could never have defeated them. But instead of one absolute dictator, there were now two kings, Darius and Cyrus, the Medes and the Persians. Before they made any kind of military, economic, or political move, they had to agree, which made it harder than having just one ruler. The flow of the image continues, and later the next kingdom from secular history was Greece under Alexander the Great, whose kingdom was divided among four generals after his death at age 33.