The invention relates to a transmission (1) for a vehicle. The transmission comprises a first input shaft (2) rotatable about a geometric axis (3), a second input shaft (4) and a clutch (5) by which clutch the first input shaft and the second input shaft are selectively connectable to an engine (6), and an output shaft (9) connectable to a final drive (18). The first input shaft (2) is connectable to the output shaft (9) and the second input shaft (4) is connectable to the output shaft (9), and the transmission further comprises an electric machine (15) connected to the first input shaft (2). A rotor of the electric machine (15) is arranged on the first input shaft (2) for rotating about said geometric axis (3), and the transmission further comprises a dog clutch (10) arranged on the first input shaft (2) for connecting and disconnecting the first input shaft to/from the output shaft (9)