# Extensions 1→N→G→Q→1 with N=C23 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C23 and Q=C2×C3⋊S3
dρLabelID
C24×C3⋊S3144C2^4xC3:S3288,1044

Semidirect products G=N:Q with N=C23 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C23⋊(C2×C3⋊S3) = C22×C3⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2336C2^3:(C2xC3:S3)288,1034
C232(C2×C3⋊S3) = C6213D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2372C2^3:2(C2xC3:S3)288,794
C233(C2×C3⋊S3) = C3282+ 1+4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2372C2^3:3(C2xC3:S3)288,1009
C234(C2×C3⋊S3) = C2×D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2372C2^3:4(C2xC3:S3)288,1007
C235(C2×C3⋊S3) = C22×C327D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3:5(C2xC3:S3)288,1017

Non-split extensions G=N.Q with N=C23 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C23.1(C2×C3⋊S3) = A4⋊Dic6φ: C2×C3⋊S3/C6S3 ⊆ Aut C23726-C2^3.1(C2xC3:S3)288,907
C23.2(C2×C3⋊S3) = C4×C3⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C23366C2^3.2(C2xC3:S3)288,908
C23.3(C2×C3⋊S3) = C12⋊S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C23366+C2^3.3(C2xC3:S3)288,909
C23.4(C2×C3⋊S3) = C2×C6.7S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C2372C2^3.4(C2xC3:S3)288,916
C23.5(C2×C3⋊S3) = (C2×C6)⋊4S4φ: C2×C3⋊S3/C6S3 ⊆ Aut C23366C2^3.5(C2xC3:S3)288,917
C23.6(C2×C3⋊S3) = C62.110D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2372C2^3.6(C2xC3:S3)288,281
C23.7(C2×C3⋊S3) = C62.38D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C2372C2^3.7(C2xC3:S3)288,309
C23.8(C2×C3⋊S3) = C62.223C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.8(C2xC3:S3)288,736
C23.9(C2×C3⋊S3) = C62.227C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.9(C2xC3:S3)288,740
C23.10(C2×C3⋊S3) = C62.228C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.10(C2xC3:S3)288,741
C23.11(C2×C3⋊S3) = C62.229C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.11(C2xC3:S3)288,742
C23.12(C2×C3⋊S3) = C62.72D4φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.12(C2xC3:S3)288,792
C23.13(C2×C3⋊S3) = C62.254C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.13(C2xC3:S3)288,793
C23.14(C2×C3⋊S3) = C62.256C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.14(C2xC3:S3)288,795
C23.15(C2×C3⋊S3) = C62.258C23φ: C2×C3⋊S3/C32C22 ⊆ Aut C23144C2^3.15(C2xC3:S3)288,797
C23.16(C2×C3⋊S3) = C62.221C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.16(C2xC3:S3)288,734
C23.17(C2×C3⋊S3) = C626Q8φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.17(C2xC3:S3)288,735
C23.18(C2×C3⋊S3) = C22⋊C4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2372C2^3.18(C2xC3:S3)288,737
C23.19(C2×C3⋊S3) = C62.225C23φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.19(C2xC3:S3)288,738
C23.20(C2×C3⋊S3) = C6212D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C2372C2^3.20(C2xC3:S3)288,739
C23.21(C2×C3⋊S3) = C62.69D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.21(C2xC3:S3)288,743
C23.22(C2×C3⋊S3) = D4×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.22(C2xC3:S3)288,791
C23.23(C2×C3⋊S3) = C6214D4φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.23(C2xC3:S3)288,796
C23.24(C2×C3⋊S3) = C2×C12.D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C23144C2^3.24(C2xC3:S3)288,1008
C23.25(C2×C3⋊S3) = C6210Q8φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.25(C2xC3:S3)288,781
C23.26(C2×C3⋊S3) = C62.247C23φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.26(C2xC3:S3)288,783
C23.27(C2×C3⋊S3) = C4×C327D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.27(C2xC3:S3)288,785
C23.28(C2×C3⋊S3) = C62.129D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.28(C2xC3:S3)288,786
C23.29(C2×C3⋊S3) = C6219D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.29(C2xC3:S3)288,787
C23.30(C2×C3⋊S3) = C2×C625C4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.30(C2xC3:S3)288,809
C23.31(C2×C3⋊S3) = C6224D4φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C2372C2^3.31(C2xC3:S3)288,810
C23.32(C2×C3⋊S3) = C2×C12.59D6φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C23144C2^3.32(C2xC3:S3)288,1006
C23.33(C2×C3⋊S3) = C62.15Q8central extension (φ=1)288C2^3.33(C2xC3:S3)288,306
C23.34(C2×C3⋊S3) = C2×C4×C3⋊Dic3central extension (φ=1)288C2^3.34(C2xC3:S3)288,779
C23.35(C2×C3⋊S3) = C2×C6.Dic6central extension (φ=1)288C2^3.35(C2xC3:S3)288,780
C23.36(C2×C3⋊S3) = C2×C12⋊Dic3central extension (φ=1)288C2^3.36(C2xC3:S3)288,782
C23.37(C2×C3⋊S3) = C2×C6.11D12central extension (φ=1)144C2^3.37(C2xC3:S3)288,784
C23.38(C2×C3⋊S3) = C22×C324Q8central extension (φ=1)288C2^3.38(C2xC3:S3)288,1003
C23.39(C2×C3⋊S3) = C22×C4×C3⋊S3central extension (φ=1)144C2^3.39(C2xC3:S3)288,1004
C23.40(C2×C3⋊S3) = C22×C12⋊S3central extension (φ=1)144C2^3.40(C2xC3:S3)288,1005
C23.41(C2×C3⋊S3) = C23×C3⋊Dic3central extension (φ=1)288C2^3.41(C2xC3:S3)288,1016

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