A conveying device is located inside a clutch device to amplify a fluid flow in an axial direction, i.e. parallel to a rotation axis of the clutch device, and hence the fluid flow can be kept sufficiently great even in the moved portions of a fluid line. The conveying device can be used in clutch devices which are arranged as separating clutches in a hybrid module. The conveying device allows even the complicated fluid lines within hybrid modules to be supplied with sufficient fluid at all times. The conveying device may be arranged at least on the first or second clutch side, and hence the quantity of conveyed fluid is dependent on the rotation speed.