Hybrid drive having an automated change-speed gearbox for a motor vehicle, the hybrid drive comprising: - an internal combustion engine and an electric machine, - a first gearbox input shaft which is drive-connected to the internal combustion engine in a non-switchable manner, wherein no starting element is situated between the internal combustion engine and the gearbox input shaft, and wherein the first gearbox input shaft is designed as a solid shaft, - a second gearbox input shaft which is arranged coaxially to the first gearbox input shaft and which is drive-connected to the electric machine, wherein the second gearbox input shaft is designed as a hollow shaft, - a gearbox output shaft (W2/W4), - a first unsynchronized dog clutch which can assume a first position (li), a second position (re) and a neutral position, and a second unsynchronized dog clutch which can assume a first position (li), a second position (re) and a neutral position, - not more than three gear set planes (Z1, Z2, Z3) for three forward gears (1G, 2G, 3G) which can be selected via the two unsynchronized dog clutches (S1, S2), wherein - a first gear set plane for providing a first forward gear is formed by a first fixed gear connected to the second gearbox input shaft for conjoint rotation and by a first movable gear meshing with the first fixed gear and arranged rotatably on the gearbox output shaft (W2/W4), - a second gear set plane for providing a third forward gear is formed by a second fixed gear connected to the second gearbox input shaft for conjoint rotation and by a second movable gear meshing with the second fixed gear and arranged rotatably on the gearbox output shaft (W2/W4), - a third gear set plane for providing a second forward gear is formed by a third movable gear arranged rotatably on the first gearbox input shaft and by a third fixed gear meshing with the third movable gear and connected to the gearbox output shaft (W2/W4) for conjoint rotation, - the first unsynchronized dog clutch is arranged on the first gearbox input shaft between the second gear set plane and the third gear set plane and is designed, in the first position (li), to connect the second fixed gear to the first gearbox input shaft, with the result that the electric machine is connected to the internal combustion engine via the first unsynchronized dog clutch, such that the electric machine can be driven by the internal combustion engine as a generator, and, in the second position (re), to connect the third movable gear to the first gearbox input shaft, - the second unsynchronized dog clutch is arranged on the gearbox output shaft (W2/W4) between the first gear set plane (Z1 and the second gear set plane and is designed to disconnect the first movable gear and the second movable gear from the gearbox output shaft (W2/W4) when the second unsynchronized dog clutch is in the neutral position. - an internal combustion engine and an electric machine, - a first gearbox input shaft which is drive-connected to the internal combustion engine in a non-switchable manner, wherein no starting element is situated between the internal combustion engine and the gearbox input shaft, and wherein the first gearbox input shaft is designed as a solid shaft, - a second gearbox input shaft which is arranged coaxially to the first gearbox input shaft and which is drive-connected to the electric machine, wherein the second gearbox input shaft is designed as a hollow shaft, - a gearbox output shaft (W2/W4), - a first unsynchronized dog clutch which can assume a first position (li), a second position (re) and a neutral position, and a second unsynchronized dog clutch which can assume a first position (li), a second position (re) and a neutral position, - not more than three gear set planes (Z1, Z2, Z3) for three forward gears (1G, 2G, 3G) which can be selected via the two unsynchronized dog clutches (S1, S2), - a first gear set plane for providing a first forward gear is formed by a first fixed gear connected to the second gearbox input shaft for conjoint rotation and by a first movable gear meshing with the first fixed gear and arranged rotatably on the gearbox output shaft (W2/W4), - a second gear set plane for providing a third forward gear is formed by a second fixed gear connected to the second gearbox input shaft for conjoint rotation and by a second movable gear meshing with the second fixed gear and arranged rotatably on the gearbox output shaft (W2/W4), - a third gear set plane for providing a second forward gear is formed by a third movable gear arranged rotatably on the first gearbox input shaft and by a third fixed gear meshing with the third movable gear and connected to the gearbox output shaft (W2/W4) for conjoint rotation, - the first unsynchronized dog clutch is arranged on the first gearbox input shaft between the second gear set plane and the third gear set plane and is designed, in the first position (li), to connect the second fixed gear to the first gearbox input shaft, with the result that the electric machine is connected to the internal combustion engine via the first unsynchronized dog clutch, such that the electric machine can be driven by the internal combustion engine as a generator, and, in the second position (re), to connect the third movable gear to the first gearbox input shaft, - the second unsynchronized dog clutch is arranged on the gearbox output shaft (W2/W4) between the first gear set plane (Z1 and the second gear set plane and is designed to disconnect the first movable gear and the second movable gear from the gearbox output shaft (W2/W4) when the second unsynchronized dog clutch is in the neutral position.