^That was the outset, Robert
. It's a "What if the Nazis had won" scenario.
There have been numerous such scenarios but this is the first so far that deals with spacefare. Interesting, and I love the Hugin & Munin names (great idea =) ).
It's, however, very difficult to predict something that might have happened (because it might just as well not have happened).
During and immediately after the war our best scientists were... hmm... let's call it "exported" to the US where they were a major factor in the American rocket programme. That might at a first glance make a similar development in Germany plausible if
Germany had ever had an interest in space travel.
And, I think, that's the point where the speculation deviates from reality: none of the prominent Nazis was interested in going into space. It's a luxury and you need time and money for that. First things first and in space there's nothing you can dominate or make money from (at least not in our immediate neighbourhood).
I think they'd first have restored the economy and infrastructure in their own country. Then in the subjugated states in order to create markets for their own economy. Only after that they'd have started to develop other interests but in my opinion they'd have stuck to more down-to-earth science (pardon the pun) like theoretical physics, mathematics and engineering. Building automats/robots, improving vehicles, that kind of stuff. There'd very likely also have been a major progress in sports, film making, radio, photography, theatre and music and to a lesser extent in painting and literature: a people that's kept busy and happy doesn't think of revolutions.
As a general rule dictatorships tend to be extremely conservative. Science and invention of any kind require a freedom of thinking that is dangerous because it doesn't remain restricted to the desired topics.