A transmission unit for a motor vehicle is provided with a fixed supporting structure, a driving transmission shaft and at least one driven transmission shaft that are parallel to one another, and a control device, which has a control member that is movable with respect to the supporting structure; the control member is able to translate along a control axis between a plurality of operating positions, each associated to a corresponding range of gears, and to turn, in each operating position, about the control axis between an idle angular position and at least one engagement angular position, in which it controls engagement of a gear forming part of the range selected; the control member is set at least in part in front of an axial end of the transmission shafts.