Go to google.com to search domestic violence and immigration and deportation. You will find that domestic violence charge is deadly serious to a green card holder.
From now, do NOT leave the States. Your green card will be detained when you come back to the States if CIS has this information.
If you are found guilty and you have had green card for at least five years and , you may manage to stay in US. To do that, you have to find a lawyer specialized in deportation.
Again remember that your immigration status is on the line now.
Wish you good luck.