Ironic that both the Nazis and the 45th used the same symbol. Then the 45th changed to something more indicative of Oklahoma’s native American heritage.
Oh yeah... Recommended reading, “From Swastika to Thunderbird”, a history of the 45th Division.
To summarize... Believe it or not, the swastika is a Native American symbol. It just has a different meaning in Native American lore other than "National Socialist Party".
My understanding is that it's associated with a sense of family and community, derived from logs in a campfire. Google some pictures of young Jackie Kennedy nee Bouvier and you'll see her as a teenager, dressed up for a costume party as an "Indian Princess", wearing a dress adorned with a Native American swastika.
I could drive you by one estate in northeastern Oklahoma that has swastikas on the gates, built before the war, and painted over to deemphasize them during the war.
So the swastika was actually every bit as Native American a symbol as the Thunderbird, although the Thunderbird was, and still is, an infinitely better unit insignia for obvious reasons.
No man has ever seen the Thunderbird and lived to tell about it, you know. :)