# Extensions 1→N→G→Q→1 with N=C32 and Q=S3×C23

Direct product G=N×Q with N=C32 and Q=S3×C23
dρLabelID
S3×C2×C62144S3xC2xC6^2432,772

Semidirect products G=N:Q with N=C32 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C32⋊(S3×C23) = C22×C32⋊D6φ: S3×C23/C22D6 ⊆ Aut C3236C3^2:(S3xC2^3)432,545
C322(S3×C23) = C23×C32⋊C6φ: S3×C23/C23S3 ⊆ Aut C3272C3^2:2(S3xC2^3)432,558
C323(S3×C23) = C23×He3⋊C2φ: S3×C23/C23S3 ⊆ Aut C3272C3^2:3(S3xC2^3)432,561
C324(S3×C23) = C2×S33φ: S3×C23/D6C22 ⊆ Aut C32248+C3^2:4(S3xC2^3)432,759
C325(S3×C23) = C22×S3×C3⋊S3φ: S3×C23/C2×C6C22 ⊆ Aut C3272C3^2:5(S3xC2^3)432,768
C326(S3×C23) = C22×C324D6φ: S3×C23/C2×C6C22 ⊆ Aut C3248C3^2:6(S3xC2^3)432,769
C327(S3×C23) = S32×C2×C6φ: S3×C23/C22×S3C2 ⊆ Aut C3248C3^2:7(S3xC2^3)432,767
C328(S3×C23) = C3⋊S3×C22×C6φ: S3×C23/C22×C6C2 ⊆ Aut C32144C3^2:8(S3xC2^3)432,773
C329(S3×C23) = C23×C33⋊C2φ: S3×C23/C22×C6C2 ⊆ Aut C32216C3^2:9(S3xC2^3)432,774

Non-split extensions G=N.Q with N=C32 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C32.(S3×C23) = C23×C9⋊C6φ: S3×C23/C23S3 ⊆ Aut C3272C3^2.(S3xC2^3)432,559
C32.2(S3×C23) = C22×S3×D9φ: S3×C23/C2×C6C22 ⊆ Aut C3272C3^2.2(S3xC2^3)432,544
C32.3(S3×C23) = D9×C22×C6φ: S3×C23/C22×C6C2 ⊆ Aut C32144C3^2.3(S3xC2^3)432,556
C32.4(S3×C23) = C23×C9⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C32216C3^2.4(S3xC2^3)432,560

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