I took a chance & stuck ours in the washing machine on a 'delicates' load. I just used a tiny amount of washing soda. It is still a bit grubby, but it seems to have survived.
My biggest tip to you is to dry it outside...it WILL smell like a wet sheep! Try to dry it flat, ie over a frame of some sort, rather than just over the line. (You'll be surprized just how heavy it will be when wet.) I used a mini greenhouse frame laid on it's side.
If it isn't a Greyhound, it's just a dog!