A powershift transmission of a motor vehicle has a split group with a plurality of powershift stages. An input shaft can be rotatably driven by a drive shaft of a motorized drive and transmits rotational movement in a stepped-up manner to an output shaft of the split group corresponding to one of several powershiftable stage transmissions. The powershiftable stage transmissions can be rotatably driven in a stepped-up manner by the output shaft of the split group via an intermediate group located therebetween, and via an input shaft of a synchromesh transmission group having a plurality of gear stages. A vehicle axle transmission can be rotatably driven by the output shaft of the synchromesh transmission group. The intermediate group has a multiple powershift intermediate transmission, in which each switching position the input shaft of the synchromesh transmission group can be rotatably driven by means of an associated transmission.