Gearbox for a vehicle and vehicle, comprising such a gearbox

A vehicle comprising a gearbox, wherein said gearbox comprises:

• a planetary gear with a ring gear;
• a sun wheel;
• a planetary wheel carrier, on which at least one planetary wheel is mounted in a rotatable manner, which ring gear and sun wheel engage with the at least one planetary wheel through teeth;
• a first axially shiftable coupling sleeve, which is arranged to disconnect an input shaft to the gearbox from the planetary wheel carrier in a first gear position of the gearbox, and to connect the input shaft with the planetary wheel carrier in a second gear position of the gearbox;
• a second axially shiftable coupling sleeve, which is arranged to connect a gearbox house around the planetary gear with the ring gear in the first gear position of the gearbox, and to disconnect the gearbox house from the ring gear in the second gear position of the gearbox;
• and
• a third axially shiftable coupling sleeve, which is arranged to connect the ring gear with an output shaft in a third gear position of the gearbox, so that the second axially shiftable coupling sleeve is arranged to connect the planetary wheel carrier with the gearbox house in the third gear position of the gearbox.