Transmission device for a drive train of a motor vehicle, in particular of an automobile

A transmission device for a drive train of a motor vehicle, the transmission device comprising:

• a multiple-disc coupling comprising at least one disc carrier and a disc pack with a plurality of discs arranged following each other in an axial direction of the multiple-disc coupling, wherein the plurality of discs include first and second end disks between which remaining discs of the plurality of disks are arranged;
• a first switching element configured to actuate the disc pack via the first end disc in an actuating direction extending in the axial direction of the multiple-disc coupling;
• and
• a second switching element arranged opposite the first switching element in the axial direction of the multiple-disc coupling, wherein the second end disc is supported directly on the at least one disc carrier in a support direction extending in the axial direction of the multiple-disc coupling and counter to the actuating direction and is supported directly on a component of the second switching element in the actuating direction,
• wherein the plurality of discs of the disc pack each have a first toothing engaging into a corresponding second toothing of the at least one disc carrier so that the plurality of discs of the disc pack are supported on the disc carrier in a circumferential direction of the multiple-disc coupling,
• wherein the second toothing has at least two teeth set back in the axial direction and forming a respective axial end face, and
• wherein, on the respective axial end faces, corresponding teeth of the first toothing of the second end disc are directly supported in the support direction.