Galois group search results

The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

Results (displaying both matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
4T3	$D_{4}$	$8$	$-1$	✓	$2$	$5$	$C_2$	4T3, 8T4
8T4	$D_4$	$8$	$1$	✓	$2$	$5$	$C_2$ x 3, $C_2^2$, $D_{4}$ x 2	4T3 x 2

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Results are complete for degrees $\leq 23$.