# Extensions 1→N→G→Q→1 with N=C4 and Q=C6×C3⋊S3

Direct product G=N×Q with N=C4 and Q=C6×C3⋊S3
dρLabelID
C3⋊S3×C2×C12144C3:S3xC2xC12432,711

Semidirect products G=N:Q with N=C4 and Q=C6×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C41(C6×C3⋊S3) = C3×D4×C3⋊S3φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C472C4:1(C6xC3:S3)432,714
C42(C6×C3⋊S3) = C6×C12⋊S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C4144C4:2(C6xC3:S3)432,712

Non-split extensions G=N.Q with N=C4 and Q=C6×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C4.1(C6×C3⋊S3) = C3×C327D8φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C472C4.1(C6xC3:S3)432,491
C4.2(C6×C3⋊S3) = C3×C329SD16φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C472C4.2(C6xC3:S3)432,492
C4.3(C6×C3⋊S3) = C3×C3211SD16φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C4144C4.3(C6xC3:S3)432,493
C4.4(C6×C3⋊S3) = C3×C327Q16φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C4144C4.4(C6xC3:S3)432,494
C4.5(C6×C3⋊S3) = C3×C12.D6φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C472C4.5(C6xC3:S3)432,715
C4.6(C6×C3⋊S3) = C3×Q8×C3⋊S3φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C4144C4.6(C6xC3:S3)432,716
C4.7(C6×C3⋊S3) = C3×C12.26D6φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C4144C4.7(C6xC3:S3)432,717
C4.8(C6×C3⋊S3) = C3×C242S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C4144C4.8(C6xC3:S3)432,482
C4.9(C6×C3⋊S3) = C3×C325D8φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C4144C4.9(C6xC3:S3)432,483
C4.10(C6×C3⋊S3) = C3×C325Q16φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C4144C4.10(C6xC3:S3)432,484
C4.11(C6×C3⋊S3) = C6×C324Q8φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C4144C4.11(C6xC3:S3)432,710
C4.12(C6×C3⋊S3) = C3⋊S3×C24central extension (φ=1)144C4.12(C6xC3:S3)432,480
C4.13(C6×C3⋊S3) = C3×C24⋊S3central extension (φ=1)144C4.13(C6xC3:S3)432,481
C4.14(C6×C3⋊S3) = C6×C324C8central extension (φ=1)144C4.14(C6xC3:S3)432,485
C4.15(C6×C3⋊S3) = C3×C12.58D6central extension (φ=1)72C4.15(C6xC3:S3)432,486
C4.16(C6×C3⋊S3) = C3×C12.59D6central extension (φ=1)72C4.16(C6xC3:S3)432,713

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