Yep. The regular edition goes out on a Friday night in a 30 minute time slot. But they usually tape for up to two hours at the recording session the evening before, so it's not hard to do a longer edit that as Jon says, goes out on Mondays at 10:40pm (after the main evening news).
The longer edit also neatly makes a commercial hour when it gets repeated on "Dave" (or "U&Dave" as the channel has been bizarrely renamed). And yes, the topical news show, does indeed get repeated months/years after its initial airing.
QI also gets the same 30/45 minute edits treatment, with the longer version known as QI XL.
Adam