there was also a blue background variant - I think it was national guard
found it
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Most collectors are aware of the fact that, from the 1920s to the late 1930s, the shoulder patch of the 45th Infantry Division was a yellow swastika on a red square. Other patches bearing the swastika symbol are to be found in collections, where often they are identified as variants of the sleeve patch of the 45th. Steve and Dave Johnson, in their article "Rag Clippings" (ASMIC's The Trading Post, October-December 1999), present compelling evidence that many of these "swastika patches" are misidentified. The swastika patches (four of the 15 illustrated in their article) discussed in the following paragraph will alert collectors to the complexity of identifying these patches. But to fully appreciate the range of swastika patches and the units (going back to the First World War) that wore them, you will want to secure a copy of the Johnsons’s article.
SOURCE: Insigne