A powershift transmission with a dual-clutch main transmission and a downstream planetary gearset. The main transmission includes two partial transmissions and corresponding input shafts and clutches and a common output shaft. The downstream transmission has an input shaft which couples, via a third shifting element, the common output shaft and is fixed to a first planetary gearset element. The downstream transmission has an output shaft that is fixed to a second planetary gearset element. A third planetary gearset element couples a housing by way of a fourth shifting element, to obtain a low driving range of the downstream transmission, or, the downstream transmission output shaft by way of a fifth shifting element to obtain a high driving range of the downstream transmission. The common output shaft can couple, via a sixth shifting element, the third planetary gearset element, which can couple, via the fourth shifting element, the transmission housing.