A dishwasher includes a dishwashing container accommodating items to be washed. A first hydraulic arrangement is provided to wash the items by a dishwashing fluid and includes a spray device arranged in the dishwashing container, a sump arranged below the dishwashing container, a filter device configured to filter the dishwashing fluid in the dishwashing container and/or the sump, and a circulating pump configured to circulate the dishwashing fluid to the spray device. A second hydraulic arrangement is provided for cleaning the filter device by a cleaning fluid. The second hydraulic arrangement includes the filter device, the sump, a pump arrangement, a storage device for holding the cleaning fluid, a cleaning device for spraying at least one segment of the filter device with the cleaning fluid, and an auxiliary pump arranged between the storage device and the cleaning device for applying pressure to the cleaning fluid.