I've never really thought about it before, but just wondering if there were additional incentives besides exploiting antisemitism to gain power and control.

I know there was forced labor at the camps, but was there also anything similar to a private prison incentive like we see in the U.S.? Government contracts are provided, and the more people you hold in your prison (or at least process as entering the prison) the bigger the government contract, and higher the profits.

What about transportation companies that owned the trains that transported people to the camps?
Was everything already purchased (or confiscated) and owned by the government when they used it to imprison people, or did they contract out to private businesses?

If everything was property of the government rather than privately held, who decided where money would be allocated, and how were the decisions made?