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Found this overview. It gives a very detailed overview:
https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Bildung-Forschung-Kultur/Hochschulen/Publikationen/Downloads-Hochschulen/studierende-hochschulen-vorb-2110410198004.html
Edit: One can contact the "statistische Bundesamt" for additional data. It may require additional time and cost.
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