A hybrid drive of a motor vehicle has an internal combustion engine, an electric machine, and a transmission. The transmission is a multi-stage shifting transmission including two subtransmissions, each of which has a separate input shaft and a common output shaft. The first input shaft of a first subtransmission can be coupled and decoupled to the internal combustion engine. The second input shaft of a second subtransmission is rigidly coupled to the electric machine. Both input shafts can be coupled selectively to the common output shaft via form-locking shift elements. The first input shaft can be attached to multiple clutches in such a way that when a first friction-locking or form-locking clutch and a second friction-locking clutch connected in series are both engaged, the internal combustion engine is coupled to the first input shaft and to the first subtransmission.