I was hopeless at algebra, so maybe that is my problem...
(If everything is "nice") the subgroups of G(E/F) correspond to intermediate fields between E and F, depending on which r_i they stabilize.
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Starting from G(C/R) gives an intuition I didn’t remember and may or may not have gotten at the time…
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That doesn’t give an intermediate field; https://en.wikipedia.org/wiki/Fundamental_theorem_of_Galois_theory … uses Q(√2,√3) which is quite intuitive
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That's the one I remember, but course was contextless 'bla bla splitting field bla solvable group bla'. Understanding something this time!
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Also I followed my usual method earlier and looked up what John Baez had to say: http://math.ucr.edu/home/baez/week201.html …
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.