# Extensions 1→N→G→Q→1 with N=C32 and Q=S3×C2×C4

Direct product G=N×Q with N=C32 and Q=S3×C2×C4
dρLabelID
S3×C6×C12144S3xC6xC12432,701

Semidirect products G=N:Q with N=C32 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C321(S3×C2×C4) = C4×C32⋊D6φ: S3×C2×C4/C4D6 ⊆ Aut C32366C3^2:1(S3xC2xC4)432,300
C322(S3×C2×C4) = C2×C6.S32φ: S3×C2×C4/C22D6 ⊆ Aut C3272C3^2:2(S3xC2xC4)432,317
C323(S3×C2×C4) = C2×He3⋊(C2×C4)φ: S3×C2×C4/C22D6 ⊆ Aut C3272C3^2:3(S3xC2xC4)432,321
C324(S3×C2×C4) = C2×C4×C32⋊C6φ: S3×C2×C4/C2×C4S3 ⊆ Aut C3272C3^2:4(S3xC2xC4)432,349
C325(S3×C2×C4) = C2×C4×He3⋊C2φ: S3×C2×C4/C2×C4S3 ⊆ Aut C3272C3^2:5(S3xC2xC4)432,385
C326(S3×C2×C4) = S3×C6.D6φ: S3×C2×C4/Dic3C22 ⊆ Aut C32248+C3^2:6(S3xC2xC4)432,595
C327(S3×C2×C4) = Dic36S32φ: S3×C2×C4/Dic3C22 ⊆ Aut C32488-C3^2:7(S3xC2xC4)432,596
C328(S3×C2×C4) = C4×S3×C3⋊S3φ: S3×C2×C4/C12C22 ⊆ Aut C3272C3^2:8(S3xC2xC4)432,670
C329(S3×C2×C4) = C4×C324D6φ: S3×C2×C4/C12C22 ⊆ Aut C32484C3^2:9(S3xC2xC4)432,690
C3210(S3×C2×C4) = C2×S3×C32⋊C4φ: S3×C2×C4/D6C4 ⊆ Aut C32248+C3^2:10(S3xC2xC4)432,753
C3211(S3×C2×C4) = S32×Dic3φ: S3×C2×C4/D6C22 ⊆ Aut C32488-C3^2:11(S3xC2xC4)432,594
C3212(S3×C2×C4) = C2×Dic3×C3⋊S3φ: S3×C2×C4/C2×C6C22 ⊆ Aut C32144C3^2:12(S3xC2xC4)432,677
C3213(S3×C2×C4) = C2×C338(C2×C4)φ: S3×C2×C4/C2×C6C22 ⊆ Aut C3272C3^2:13(S3xC2xC4)432,679
C3214(S3×C2×C4) = C2×C339(C2×C4)φ: S3×C2×C4/C2×C6C22 ⊆ Aut C3248C3^2:14(S3xC2xC4)432,692
C3215(S3×C2×C4) = S32×C12φ: S3×C2×C4/C4×S3C2 ⊆ Aut C32484C3^2:15(S3xC2xC4)432,648
C3216(S3×C2×C4) = C6×C6.D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C3248C3^2:16(S3xC2xC4)432,654
C3217(S3×C2×C4) = C3⋊S3×C2×C12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C32144C3^2:17(S3xC2xC4)432,711
C3218(S3×C2×C4) = C2×C4×C33⋊C2φ: S3×C2×C4/C2×C12C2 ⊆ Aut C32216C3^2:18(S3xC2xC4)432,721
C3219(S3×C2×C4) = S3×C6×Dic3φ: S3×C2×C4/C22×S3C2 ⊆ Aut C3248C3^2:19(S3xC2xC4)432,651
C3220(S3×C2×C4) = C2×S3×C3⋊Dic3φ: S3×C2×C4/C22×S3C2 ⊆ Aut C32144C3^2:20(S3xC2xC4)432,674

Non-split extensions G=N.Q with N=C32 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C32.(S3×C2×C4) = C2×C4×C9⋊C6φ: S3×C2×C4/C2×C4S3 ⊆ Aut C3272C3^2.(S3xC2xC4)432,353
C32.2(S3×C2×C4) = C4×S3×D9φ: S3×C2×C4/C12C22 ⊆ Aut C32724C3^2.2(S3xC2xC4)432,290
C32.3(S3×C2×C4) = C2×Dic3×D9φ: S3×C2×C4/C2×C6C22 ⊆ Aut C32144C3^2.3(S3xC2xC4)432,304
C32.4(S3×C2×C4) = C2×C18.D6φ: S3×C2×C4/C2×C6C22 ⊆ Aut C3272C3^2.4(S3xC2xC4)432,306
C32.5(S3×C2×C4) = D9×C2×C12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C32144C3^2.5(S3xC2xC4)432,342
C32.6(S3×C2×C4) = C2×C4×C9⋊S3φ: S3×C2×C4/C2×C12C2 ⊆ Aut C32216C3^2.6(S3xC2xC4)432,381

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