Can a car insurance company take out more money from your account than they are supposed to without your knowledge?

No they can't and they don't. I would be certain that you made some change to you policy like adding a vehicle or such. Either that or the insurance company found more tickets than you told them about when you took out the policy causing the premium to increase. In either case the company would have mailed you a new declarations page with the increase shown on the page as well as the increase in payments shown as well. If you didn't open the mail, or gave them the wrong address, or didn't read the declarations page, that is not the insurance company's fault. They will always notify you in plenty of time prior to the premium being deducted. Usually if the date of deduction is too close, they will even wait until the next payment to make the change so you are adequately informed.