A gearbox for a vehicle, the gearbox comprising: a gearbox casing ; a primary shaft rotationally mounted within the gearbox casing to rotate around a first axis (A1), and having first and second axial ends within the gearbox casing ; a primary input gear which is is fixed in rotation with the primary shaft ; a distribution gear which is fixed in rotation with the primary shaft ; a transmission gear , which is configured to rotate around the first axis (A1) and which is arranged around the primary shaft ; an auxiliary shaft configured to rotate around a second axis (A2), the first axis (A1) and the second axis (A2) being distant from each other, an auxiliary output gear and an auxiliary transmission gear which are arranged around the auxiliary shaft , said auxiliary transmission gear being engaged to the transmission gear ; an output gear for transmitting a power out of the gearbox, said output gear being independently and rotationally arranged around the primary shaft and being configured to rotate around the first axis (A1), said output gear being mounted on the primary shaft and being engaged to the auxiliary output gear ; a gear shift system slidable between at least two positions, said gear shift system being configured to rotationally engage: the distribution gear and the output gear for transmitting the power directly from the primary shaft to the output gear , or the distribution gear and the transmission gear for transmitting the power indirectly from the primary shaft to the output gear through the auxiliary shaft . a gearbox casing ; a primary shaft rotationally mounted within the gearbox casing to rotate around a first axis (A1), and having first and second axial ends within the gearbox casing ; a primary input gear which is is fixed in rotation with the primary shaft ; a distribution gear which is fixed in rotation with the primary shaft ; a transmission gear , which is configured to rotate around the first axis (A1) and which is arranged around the primary shaft ; an auxiliary shaft configured to rotate around a second axis (A2), the first axis (A1) and the second axis (A2) being distant from each other, an auxiliary output gear and an auxiliary transmission gear which are arranged around the auxiliary shaft , said auxiliary transmission gear being engaged to the transmission gear ; an output gear for transmitting a power out of the gearbox, said output gear being independently and rotationally arranged around the primary shaft and being configured to rotate around the first axis (A1), said output gear being mounted on the primary shaft and being engaged to the auxiliary output gear ; a gear shift system slidable between at least two positions, said gear shift system being configured to rotationally engage: the distribution gear and the output gear for transmitting the power directly from the primary shaft to the output gear , or the distribution gear and the transmission gear for transmitting the power indirectly from the primary shaft to the output gear through the auxiliary shaft . the distribution gear and the output gear for transmitting the power directly from the primary shaft to the output gear , or the distribution gear and the transmission gear for transmitting the power indirectly from the primary shaft to the output gear through the auxiliary shaft . <EOS>