Galois group search results

Results (displaying both matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
24T400	$C_2^3\times S_4$	$192$	$1$	✓	$-1$	$40$	$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $S_4\times C_2$ x 4, $S_3 \times C_2^2$, $C_2^2\times S_4$ x 6	24T400 x 55, 32T2168 x 8
32T2168	$C_2^3\times S_4$	$192$	$1$	✓	$-1$	$40$	$C_2$ x 7, $C_2^2$ x 7, $S_4$, $C_2^3$, $S_4\times C_2$ x 7, $C_2^2\times S_4$ x 7	24T400 x 56, 32T2168 x 7

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Results are complete for degrees $\leq 23$.