Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C4 and Q=C2×C3⋊S3
dρLabelID
C2×C4×C3⋊S372C2xC4xC3:S3144,169

Semidirect products G=N:Q with N=C4 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C41(C2×C3⋊S3) = D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C436C4:1(C2xC3:S3)144,172
C42(C2×C3⋊S3) = C2×C12⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C472C4:2(C2xC3:S3)144,170

Non-split extensions G=N.Q with N=C4 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C3⋊S3) = C327D8φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.1(C2xC3:S3)144,96
C4.2(C2×C3⋊S3) = C329SD16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.2(C2xC3:S3)144,97
C4.3(C2×C3⋊S3) = C3211SD16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.3(C2xC3:S3)144,98
C4.4(C2×C3⋊S3) = C327Q16φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C4144C4.4(C2xC3:S3)144,99
C4.5(C2×C3⋊S3) = C12.D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.5(C2xC3:S3)144,173
C4.6(C2×C3⋊S3) = Q8×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.6(C2xC3:S3)144,174
C4.7(C2×C3⋊S3) = C12.26D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C472C4.7(C2xC3:S3)144,175
C4.8(C2×C3⋊S3) = C242S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C472C4.8(C2xC3:S3)144,87
C4.9(C2×C3⋊S3) = C325D8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C472C4.9(C2xC3:S3)144,88
C4.10(C2×C3⋊S3) = C325Q16φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C4144C4.10(C2xC3:S3)144,89
C4.11(C2×C3⋊S3) = C2×C324Q8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C4144C4.11(C2xC3:S3)144,168
C4.12(C2×C3⋊S3) = C8×C3⋊S3central extension (φ=1)72C4.12(C2xC3:S3)144,85
C4.13(C2×C3⋊S3) = C24⋊S3central extension (φ=1)72C4.13(C2xC3:S3)144,86
C4.14(C2×C3⋊S3) = C2×C324C8central extension (φ=1)144C4.14(C2xC3:S3)144,90
C4.15(C2×C3⋊S3) = C12.58D6central extension (φ=1)72C4.15(C2xC3:S3)144,91
C4.16(C2×C3⋊S3) = C12.59D6central extension (φ=1)72C4.16(C2xC3:S3)144,171

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