The carbon footprint of doing the dishes:
Almost zero CO2e: by hand in cold water (but the plates aren't clean)
540g CO2e: by hand, using water sparingly and not too hot
770g CO2e: in a dishwasher at 55°C
990g CO2e: in a dishwasher at 65°C
8000g CO2e: by hand, with extravagant use of water
Taken from
The Guardian
So for a family of 4 a dishwasher is greener & uses LESS water. You cannot compare the use of 1 person washing up in a like for like way with a dishwasher. A couple I know use their dishwasher every 3 days or so. The equivalent to a family of 6.