Done it too, make sure you remove the metal rods from the covering material before it goes in the machine, I also broke a plastic runner thing which is attached to the seat back cover, but it still works fine.

Only thing I am not sure about, is the bum seat , taking the cover off it is a nightmare as it's glued, I took mine off, but never got round to glueing it back together, so I can't recommend what to do with that one.

PS: on the sides of the seat where the back hinges with the bottom, there are plastic covers, if you look carefully, there are holes in there (three each side I think), which are blanked by little plastic plugs.
Push the plugs out, and you should find screws or something like that behind them which will make it much easier to take the whole seat apart