Drive system for an electric vehicle and method for operating the drive system

A drive system with an electric machine including a rotor shaft, a two-stage transmission having first and second gearwheels mounted to an intermediate shaft, an oil pump mounted to the intermediate shaft, and two clutches operably disposed between the transmission and a split output shaft, wherein the first gearwheel is driven by the rotor shaft and the second gearwheel drives a drive gear mounted to a common clutch basket of the two clutches, wherein the rotor shaft, the intermediate shaft and the split output shaft are aligned to be parallel to each other, wherein the rotor shaft defines an axial overall rotor shaft length, wherein a predominant component of an axial length of the intermediate shaft and the oil pump runs within the axial overall rotor shaft length, wherein a predominant component of an axial length of the split output shaft runs within the axial overall rotor shaft length, and wherein the drive wheel extends completely below the intermediate shaft within the axial overall length of the intermediate shaft and partially below the rotor shaft within the axial overal rotor shaft length.