A gearbox for a vehicle includes a primary shaft configured to rotate about a first axis, a distribution gear, a transmission gear arranged around the primary shaft, an auxiliary shaft configured to rotate around a second axis, an auxiliary output gear and an auxiliary transmission gear arranged around the auxiliary shaft, an output gear arranged around the primary shaft for transmitting a power out of the gearbox, and a gear shift system slidable between at least two positions. The gear shift system is 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.