lost order

To check/test my shop:
I have ordered a product and entered all costumer details.
In checkout I have selected a (dutch) payment method and got to the part where you are supposed to log in to your bank.
There I have quitted the page and returned to the shop.
From the PSP I got a mail that there has been a failed payment.
In the shop I found the registrated costumer.
I have not found the order in ADMIN and did not get an orderconfirmation email with failed payment (as costumer)

Question:
Is an order only saved after completing payment sequence? (succes payment or not)

An order is generally saved after the transaction is verified. Unless the payment module does otherwise. Payment modules can save the order before the gateway using the command $order->save();