The present invention relates to a triple clutch device (2) for arrangement in a drivetrain of a motor vehicle having a double clutch device comprising a first disk clutch (40) for selective torque transmission between a first input-side disk carrier (52) and a first output-side disk carrier (54) and a second disk clutch (42) for selective torque transmission between a second input-side disk carrier (56), which is connected rotationally fixed to the first input-side disk carrier (52), and a second output-side disk carrier (58), and having a separating clutch device comprising a third disk clutch (44) for selective torque transmission between a third input-side disk carrier (60) and a third output-side disk carrier (62), wherein the first input-side disk carrier (52) is connected rotationally fixed to the third output-side disk carrier (62), and a first disk set (46) of the first disk clutch (40) and a third disk set (50) of the third disk clutch (44) are arranged nested in the radial directions (8, 10). The third disk set (50) is arranged within the first disk set (46) in the radial direction (10). The present invention additionally relates to a drivetrain of a motor vehicle comprising such a triple clutch device (2).