Transmission for a motor vehicle, the transmission having a drive shaft, an output shaft, a first, second and third planetary gear set (P1, P2, P3), and a first, second, third, fourth, fifth and sixth shifting element (03, 05, 06, 14, 17, 67), - the planetary gear sets (P1, P2, P3) in each case having a first element (E11, E12, E13), a second element (E21, E22, E23) and a third element (E31, E32, E33), the first element (E11, E12, E13) being formed by way of a sun gear of the respective planetary gear set (P1, P2, P3), the second element (E21, E22, E23) being formed by way of a spider in the case of a negative gear set and by way of an internal gear of the respective planetary gear set (P1, P2, P3) in the case of a positive gear set, the third element (E31, E32, E33) being formed by way of the internal gear in the case of a negative gear set and by way of the spider of the respective planetary gear set (P1, P2, P3) in the case of a positive gear set, - the output shaft being connected permanently to the third element of the first planetary gear set and to the second element of the third planetary gear set, - the first element of the first planetary gear set being connected permanently to the first element of the second planetary gear set, - the transmission having a first coupling and a second coupling, the first coupling existing between the first element of the third planetary gear set and a rotationally locked element of the transmission, the second coupling existing between the second element of the second planetary gear set and the third element of the third planetary gear set, one of the two couplings (V1, V2) being formed by way of a permanently rotationally locked connection, and the remaining one of the two couplings (V1, V2) being formed by way of a connection which can be selected by means of the first shifting element, - it being possible for the first element of the first planetary gear set to be fixed in a rotationally locked manner by way of closure of the second shifting element, - it being possible for the second element of the first planetary gear set to be fixed in a rotationally locked manner by way of closure of the third shifting element, - it being possible for the drive shaft to be connected to the second element of the second planetary gear set by way of closure of the fourth shifting element, - it being possible for the drive shaft to be connected to the third element of the second planetary gear set by way of closure of the fifth shifting element, - and it being possible for the second element of the first planetary gear set to be connected to the third element of the second planetary gear set by way of closure of the sixth shifting element. - the planetary gear sets (P1, P2, P3) in each case having a first element (E11, E12, E13), a second element (E21, E22, E23) and a third element (E31, E32, E33), the first element (E11, E12, E13) being formed by way of a sun gear of the respective planetary gear set (P1, P2, P3), the second element (E21, E22, E23) being formed by way of a spider in the case of a negative gear set and by way of an internal gear of the respective planetary gear set (P1, P2, P3) in the case of a positive gear set, the third element (E31, E32, E33) being formed by way of the internal gear in the case of a negative gear set and by way of the spider of the respective planetary gear set (P1, P2, P3) in the case of a positive gear set, - the output shaft being connected permanently to the third element of the first planetary gear set and to the second element of the third planetary gear set, - the first element of the first planetary gear set being connected permanently to the first element of the second planetary gear set, - the transmission having a first coupling and a second coupling, the first coupling existing between the first element of the third planetary gear set and a rotationally locked element of the transmission, the second coupling existing between the second element of the second planetary gear set and the third element of the third planetary gear set, one of the two couplings (V1, V2) being formed by way of a permanently rotationally locked connection, and the remaining one of the two couplings (V1, V2) being formed by way of a connection which can be selected by means of the first shifting element, - it being possible for the first element of the first planetary gear set to be fixed in a rotationally locked manner by way of closure of the second shifting element, - it being possible for the second element of the first planetary gear set to be fixed in a rotationally locked manner by way of closure of the third shifting element, - it being possible for the drive shaft to be connected to the second element of the second planetary gear set by way of closure of the fourth shifting element, - it being possible for the drive shaft to be connected to the third element of the second planetary gear set by way of closure of the fifth shifting element, - and it being possible for the second element of the first planetary gear set to be connected to the third element of the second planetary gear set by way of closure of the sixth shifting element.