A transmission includes a main gearbox and an electric machine. The main gearbox has a primary shaft, a secondary shaft and gear sets, each having a driving gearwheel carried by a respective primary shaft and a driven gearwheel carried by a respective secondary shaft. A first gearwheel and a second gearwheel meshing with each other are idly mounted on the primary shaft and on the secondary shaft, respectively, and are selectively connectable for rotation with the respective shaft by a first coupling device and of a second coupling device, respectively. The electric machine is releasably connected to the first gearwheel or to the second gearwheel, such that with the first coupling device in an engaged position the electric machine is able to transmit torque to the primary shaft on which the first gearwheel is mounted, while with the second coupling device in an engaged position, the electric machine is able to transmit torque to the secondary shaft on which the second gearwheel is mounted. The transmission further includes a secondary gearbox with two or more gears between the electric machine and the first or the second gearwheel.