A clutch device includes a first and a second input side as well as a first and a second output side. The input sides and the output sides can be rotated about a common axis of rotation. The clutch device furthermore includes a first clutch between the first input side and the first output side and a second clutch between the first input side and the second output side. A third clutch may be provided between the first input side and the second input side. A first hydraulic actuating device is associated with the first clutch, a second hydraulic actuating device is associated with the second clutch, and a third hydraulic actuating device is associated with the third clutch. A radial flange, which receives an axial actuating force of one of the actuating devices, includes a radially extending feed for hydraulic fluid to one of the actuating devices.