# Extensions 1→N→G→Q→1 with N=C32 and Q=C2×S4

Direct product G=N×Q with N=C32 and Q=C2×S4
dρLabelID
C3×C6×S454C3xC6xS4432,760

Semidirect products G=N:Q with N=C32 and Q=C2×S4
extensionφ:Q→Aut NdρLabelID
C32⋊(C2×S4) = C625D6φ: C2×S4/C22D6 ⊆ Aut C32186+C3^2:(C2xS4)432,523
C322(C2×S4) = C2×C62⋊S3φ: C2×S4/C23S3 ⊆ Aut C32186+C3^2:2(C2xS4)432,535
C323(C2×S4) = C2×C32⋊S4φ: C2×S4/C23S3 ⊆ Aut C32183C3^2:3(C2xS4)432,538
C324(C2×S4) = S3×C3⋊S4φ: C2×S4/A4C22 ⊆ Aut C322412+C3^2:4(C2xS4)432,747
C325(C2×S4) = C6210D6φ: C2×S4/A4C22 ⊆ Aut C322412+C3^2:5(C2xS4)432,748
C326(C2×S4) = C3×S3×S4φ: C2×S4/S4C2 ⊆ Aut C32246C3^2:6(C2xS4)432,745
C327(C2×S4) = C3⋊S3×S4φ: C2×S4/S4C2 ⊆ Aut C3236C3^2:7(C2xS4)432,746
C328(C2×S4) = C6×C3⋊S4φ: C2×S4/C2×A4C2 ⊆ Aut C32366C3^2:8(C2xS4)432,761
C329(C2×S4) = C2×C324S4φ: C2×S4/C2×A4C2 ⊆ Aut C3254C3^2:9(C2xS4)432,762

Non-split extensions G=N.Q with N=C32 and Q=C2×S4
extensionφ:Q→Aut NdρLabelID
C32.(C2×S4) = C2×C32.S4φ: C2×S4/C23S3 ⊆ Aut C32186+C3^2.(C2xS4)432,533
C32.2(C2×S4) = S3×C3.S4φ: C2×S4/A4C22 ⊆ Aut C323612+C3^2.2(C2xS4)432,522
C32.3(C2×S4) = C6×C3.S4φ: C2×S4/C2×A4C2 ⊆ Aut C32366C3^2.3(C2xS4)432,534
C32.4(C2×S4) = C2×C32.3S4φ: C2×S4/C2×A4C2 ⊆ Aut C3254C3^2.4(C2xS4)432,537

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