The invention relates to a housing (10) of an electric drive having a stator (29) and a rotor for an electric axle module of an electrically driven vehicle, comprising a cooling duct (56) through which a cooling medium flows. The cooling duct (56) is formed by a first duct geometry (16) on an inner side (13) of a sleeve-shaped extension (11) of the housing (10) and by a second duct geometry (24) configured on a casing (54) of a sleeve (28).