Hi glmr, well I can see right away that you've got a top face on your extrusion which has 24 holes in it, which right there is not suitable for subdivision smoothing.

In order to do sub-d smoothing, your object needs to be made up only of 3 or 4 sided faces with no inner holes in any of them at all. So instead of one single face on the top with trimmed holes in it, the top part of an object like that needs to be tiled and made up of a bunch of smaller 4 sided faces that sort of flow around the holes.

Also you'd typically have an angular cage-like object as the base object to be subdivided, with all edges just being line segments, not starting out with curvy outlines like you've got there.

Sub-d modeling is a really different approach from a drawing based one like you're showing there.

- Michael