The invention relates to a transmission housing (1) comprising a housing (1) body (1A) which defines an enclosure (1B) and, arranged at least partly inside said enclosure (1B), an input shaft (2), an output shaft (3) and a mechanism (4) for transmitting the movement of the input shaft (2) to the output shaft (3), this movement transmitting mechanism (4) comprising at least one clutch (5), the clutch (5) comprising a driving element (6) and a driven element (7), the driven element (7) being mounted for conjoined rotation with the output shaft (3) and comprising an active part (8) of the clutch (5) and a sleeve (9) that carries said active part (8) of the clutch (5), wherein the active part (8) of the clutch (5) is in bearing contact with the driving element (6) of the clutch (5) when the clutch (5) is in the engaged position, the sleeve (9) being coaxial to the output shaft (3) and mounted for conjoined rotation with the output shaft (3), the sleeve (9) of the driven element (7) being made in a single piece with the active part (8) of the driven element (7), and the sleeve (9) being disposed between the output shaft (3) and the body (1A) of the housing (1).