Yup, most of us (but not all) are running external filters. Just to be sure, you could follow the oil hoses from the cooler back to the engine: One (or both) should go to just below the lower fan belt pulley (that's where the oil pump is) but one of them might go into the engine case slightly higher than the pump and just to the left.
In this photo of my engine, you can see the pump (it says "Gene Berg" on mine - Gene was pretty vain) with the brass hose connector on the left side, and just above the tip of that hose connector is an open hole where my other hose goes to. You may have both hoses going into the pump cover for a different variation. The big white can on the left is my oil filter.
So, you shopping for a floor jack yet? 😉