A gearbox for a vehicle includes: a housing; first and second shafts extending parallel to one another; first transmission gears mounted to the first shaft; and second transmission gears mounted to the second shaft. The transmission gears are helical gears. The first transmission gears are in constant mesh with the second transmission gears to form a plurality of gear pairings engageable to operate the gearbox in different gears. A drive gear is mounted to an input shaft extending into the housing. The input shaft is operatively connected to an engine of the vehicle. A driven gear is mounted to the second shaft and is configured to engage the drive gear. The drive and driven gears are spur gears. A flexible driving member is configured to drivingly connect one of the first shaft and the second shaft to an output shaft. A snowmobile including a gearbox is also contemplated.