A clutch assembly for a drive train of a motor vehicle, wherein the clutch assembly comprises: - a housing, - a carrier body mounted rotatably about an axis of rotation relative to the housing, wherein the axis of rotation extends from an engine side to a transmission side of the clutch assembly, - a first clutch, which comprises a first first-clutch component via the carrier body for rotationally fixed connection to an input shaft and a second first-clutch component that is rotatably connectable to the first first-clutch component, - a second clutch, which comprises two second-clutch components (26, 28) that are rotatably connectable to one another and which is arranged in a rotationally fixed manner with a first second-clutch component on the second first-clutch component of the first clutch, and which can be connected with a second second-clutch component to a first output shaft, and - wherein a common support body is arranged on the first clutch and on the second clutch, which common support body abuts the first clutch and the second clutch against axial loads along the axis of rotation, wherein the axial loads of the first clutch act from a transmission-side first pressure pot to the clutch operative connection and the axial loads of the second clutch act from a transmission-side second pressure pot to the clutch operative connection, characterized in that - a third clutch is provided, which comprises two third-clutch components (32, 34) that are rotatably connectable to one another and which is arranged in a rotationally fixed manner with a first third-clutch component on the second first-clutch component of the first clutch, and which can be connected with a second third-clutch component to a second output shaft. - a housing, - a carrier body mounted rotatably about an axis of rotation relative to the housing, wherein the axis of rotation extends from an engine side to a transmission side of the clutch assembly, - a first clutch, which comprises a first first-clutch component via the carrier body for rotationally fixed connection to an input shaft and a second first-clutch component that is rotatably connectable to the first first-clutch component, - a second clutch, which comprises two second-clutch components (26, 28) that are rotatably connectable to one another and which is arranged in a rotationally fixed manner with a first second-clutch component on the second first-clutch component of the first clutch, and which can be connected with a second second-clutch component to a first output shaft, and - wherein a common support body is arranged on the first clutch and on the second clutch, which common support body abuts the first clutch and the second clutch against axial loads along the axis of rotation, wherein the axial loads of the first clutch act from a transmission-side first pressure pot to the clutch operative connection and the axial loads of the second clutch act from a transmission-side second pressure pot to the clutch operative connection, characterized in that - a third clutch is provided, which comprises two third-clutch components (32, 34) that are rotatably connectable to one another and which is arranged in a rotationally fixed manner with a first third-clutch component on the second first-clutch component of the first clutch, and which can be connected with a second third-clutch component to a second output shaft.