Friction disc system for a wet friction clutch having a first friction disc and a second friction disc, - it being possible for the first friction disc to be coupled to an input side of a friction clutch and for the second friction disc to be coupled to an output side of the friction clutch, - each friction disc (20, 25) in each case having a carrier disc (80, 85) and a friction lining (100, 105) which is arranged on the front side of the carrier disc (80, 85), - the two friction discs (20, 25) being arranged so as to adjoin one another axially in such a way that the carrier disc of the first friction disc is arranged so as to lie axially opposite the friction lining of the second friction disc, - the carrier discs (80, 85) and the friction lining (100, 105) being configured to be pressed onto one another, in order to provide a frictionally locking connection between the friction lining of the first friction disc and the carrier disc of the second friction disc and to connect the input side to the output side in a torque-locking manner, - in each case at least one radial groove (115, 150) being provided in the friction lining (100, 105) of the first and the second friction disc (20, 25), which radial groove (115, 150) is guided at least partially radially from the inside to the outside and is configured to conduct a cooling liquid of the friction clutch for cooling the friction discs (20, 25), at least one through opening which runs at least partially in the radial direction from the outside to the inside being provided in the carrier disc (80, 85) of the first and/or second friction disc (20, 25), - the through opening fluidically connecting the radial groove of the first friction disc to the radial groove of the second friction disc, with the result that the cooling liquid can flow from the radial groove of the second friction disc into the radial groove of the first friction disc, characterized in that a further radial groove and a connecting groove are provided in the friction lining of the second friction disc, the further radial groove being arranged so as to run at least partially radially from the inside to the outside and so as to be spaced apart on the circumferential side from the radial groove, the connecting groove being configured so as to run around at least partially in the circumferential direction and fluidically connecting the radial groove to the further radial groove. - it being possible for the first friction disc to be coupled to an input side of a friction clutch and for the second friction disc to be coupled to an output side of the friction clutch, - each friction disc (20, 25) in each case having a carrier disc (80, 85) and a friction lining (100, 105) which is arranged on the front side of the carrier disc (80, 85), - the two friction discs (20, 25) being arranged so as to adjoin one another axially in such a way that the carrier disc of the first friction disc is arranged so as to lie axially opposite the friction lining of the second friction disc, - the carrier discs (80, 85) and the friction lining (100, 105) being configured to be pressed onto one another, in order to provide a frictionally locking connection between the friction lining of the first friction disc and the carrier disc of the second friction disc and to connect the input side to the output side in a torque-locking manner, - in each case at least one radial groove (115, 150) being provided in the friction lining (100, 105) of the first and the second friction disc (20, 25), which radial groove (115, 150) is guided at least partially radially from the inside to the outside and is configured to conduct a cooling liquid of the friction clutch for cooling the friction discs (20, 25), at least one through opening which runs at least partially in the radial direction from the outside to the inside being provided in the carrier disc (80, 85) of the first and/or second friction disc (20, 25), - the through opening fluidically connecting the radial groove of the first friction disc to the radial groove of the second friction disc, with the result that the cooling liquid can flow from the radial groove of the second friction disc into the radial groove of the first friction disc, characterized in that