Very wise mathematician once said, roughly: "In the beginning there were i and -i. But we don't know which is which. That's Galois theory."
...is actually an anti-isomorphism between the subgroup poset and the poset of intermediate fields.
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I was going to say to
@drossbucket last night that “I think there was a picture and if you get the picture you get the idea,” and > -
I think the mental picture of the two lattices being upside-down from each other is what I was failing to remember
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.