World War II was the bloodiest war that has ever taken place on this planet. The death toll of this war reaches from 50 million to 80 million. It lasted 6 years starting from 1939 and ending with Hitler's death, Allied victory in 1945. It is estimated that this death toll would've been a lot higher if the Nazis had won.
Nazis conducted experiments on live human subjects, forced Jews into labor camps, exterminated them in concentration camps. To save money, they used gasses. Things had gotten so bad that they are stories of how Nazis killed toddlers with the stocks of their guns, so that their bullets won't go to waste. This is not even scratches the surface of that humongous iceberg of Nazi war crimes that stretches so far underwater that it is unimaginable.
The extermination and enslavement of "inferior" races, handicapped people, homosexuals, transvestites, transsexuals, gravely ill people, enslavement of the continent of Africa the list goes on. These are what the Nazis had in mind in their quest to "cleanse" the world of the "inferior" and make it the haven of the "superior". So, basically remorseless extermination, enslavement, and "cleansing". "The Final Solution."
Those were some of the goals of Nazis. Being human, who are filled with curiosity and are blessed with something called imagination, this information entices us to imagine what would happen if Nazis had won the World War and Allies had lost.
The Total Extermination
Auschwitz concentration camp.
All the Jewish people would be hunted, and murdered. That's the first thing they'd do, really. Any and all inferior races would be sent into concentration camps or they would be sent to forced labour camps. Frankly, death is a better fate than working in a labour camps for the Nazis.
Jewish people would be forced into hiding, they'd be afraid to call themselves Jewish. They would not be able to trust anyone in that world because if their neighbor or friend disregards it, he himself may be in danger of being hunted. And people value their own lives more than anyone else's. Bounties would be placed and bounty hunters and mercenaries would come into the picture, as if the Nazis weren't enough themselves. They would hunt the Jewish people till the end of time. I'm not even exaggerating. With the passage of time, the basic idea of Nazism would be engraved into the minds of people, and even some who showed hesitation would eventually become followers of that same idea.
The whole continent of Africa would be subjected to enslavement. Africa is pretty big so it would take Nazis quite a while to capture the whole of it. Resistances would be formed, and some may even have success. A few African could stay independent, it's possible. But it would only be temporary and not permanent.
The Continuation of Rule
The Nazi rule wouldn't end anytime soon. It is a common misconception that empires end when their leader dies. That may happen when the empires themselves are based on the strength of military and not on some idea or solid politics. Take Alexander the Great. He captured half the world, give or take. But soon after his death, his empire collapsed.
Nazism is a based on an idea. However twisted, sick, and horrific it may be, it's based on an idea. And ideas don't die. People die, ideas don't. People think that if Hitler was assassinated during World War II, or even before that, Allies would have easily won. But it's a huge misconception. Hitler was a terrible strategist and Allies feared that anyone who succeeded him would be much better which is why they didn't assassinate him. They had even planned out the operation, but ultimately decided not to go ahead with it.
It's like Hydra. Cut off one head and two more shall take it's place. Hitler dies, so what? He had thousands of others ready to take his place, with many of them better at things he wasn't.
The rule would've continued and only would have come to an end if there was a successful enough revolution. But I doubt that this would be the case. Nazis were ruthless, stopping at nothing to protect their rule and power, so I doubt that a revolution would've succeeded.
Conclusion
A Nazi regime would've been the worst thing to ever happen to humanity. I shudder at even the very thought of being under the tyrannical rule of the Nazis. America would've been completely captured, Berlin would be the capital of the world. I imagine that the Nazi brain-washing would start at the school-level. It'd evolve to such a point where it would be considered commonplace, and "right" to look down upon all those who were considered "inferior" by the Nazis.
To sum it up, there would be a complete extermination and enslavement of "inferior" races and other people with however minute disabilities, people lacking the superior "Aryan features". There are a few amazing books that depict this rule, I'd recommend reading Fatherland, and The Man In The High Castle.
Nazism is an idea, and ideas don't die however hard we may want them to. Even today, the world is not devoid of Nazi sympathizers. It is not devoid of antisemitism, and Neo-Nazis. One way of looking at how a Nazi-occupied world would be: a socially, religiously, and politically converse of today's world. Nazism is not tolerated today, it would be celebrated of course in a Nazi-occupied world. Diversity is celebrated, it would not be tolerated. Racism is not tolerated, it would be celebrated. Some think that Nazis would be far more advanced in technology than we are right now if they were in rule. Which may be hypothetically possible as they were involved in some pretty dark research and development programmes. They were power hungry, and power makes people mad. However much they had attained power, there would still be a void in their stomach for one thing: Power. And the quest for power is never-ending. It takes you to the moon, and beyond. After all, the Americans only got to the Moon because they were involved in a space-race with the Soviets. If they hadn't, I imagine things would be different.
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