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Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C3⋊Dic3

Direct product G=N×Q with N=C6 and Q=C2×C3⋊Dic3
dρLabelID
C2×C6×C3⋊Dic3144C2xC6xC3:Dic3432,718

Semidirect products G=N:Q with N=C6 and Q=C2×C3⋊Dic3
extensionφ:Q→Aut NdρLabelID
C6⋊1(C2×C3⋊Dic3) = C2×S3×C3⋊Dic3φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6:1(C2xC3:Dic3)432,674
C6⋊2(C2×C3⋊Dic3) = C22×C33⋊5C4φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6:2(C2xC3:Dic3)432,728

Non-split extensions G=N.Q with N=C6 and Q=C2×C3⋊Dic3
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C3⋊Dic3) = S3×C32⋊4C8φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6.1(C2xC3:Dic3)432,430
C6.2(C2×C3⋊Dic3) = C33⋊7M4(2)φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6.2(C2xC3:Dic3)432,433
C6.3(C2×C3⋊Dic3) = Dic3×C3⋊Dic3φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6.3(C2xC3:Dic3)432,448
C6.4(C2×C3⋊Dic3) = C62.77D6φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6.4(C2xC3:Dic3)432,449
C6.5(C2×C3⋊Dic3) = C62.80D6φ: C2×C3⋊Dic3/C3⋊Dic3 → C2 ⊆ Aut C6144C6.5(C2xC3:Dic3)432,452
C6.6(C2×C3⋊Dic3) = C2×C36.S3φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.6(C2xC3:Dic3)432,178
C6.7(C2×C3⋊Dic3) = C36.69D6φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6216C6.7(C2xC3:Dic3)432,179
C6.8(C2×C3⋊Dic3) = C4×C9⋊Dic3φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.8(C2xC3:Dic3)432,180
C6.9(C2×C3⋊Dic3) = C36⋊Dic3φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.9(C2xC3:Dic3)432,182
C6.10(C2×C3⋊Dic3) = C62.127D6φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6216C6.10(C2xC3:Dic3)432,198
C6.11(C2×C3⋊Dic3) = C22×C9⋊Dic3φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.11(C2xC3:Dic3)432,396
C6.12(C2×C3⋊Dic3) = C2×C33⋊7C8φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.12(C2xC3:Dic3)432,501
C6.13(C2×C3⋊Dic3) = C33⋊18M4(2)φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6216C6.13(C2xC3:Dic3)432,502
C6.14(C2×C3⋊Dic3) = C4×C33⋊5C4φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.14(C2xC3:Dic3)432,503
C6.15(C2×C3⋊Dic3) = C62.147D6φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6432C6.15(C2xC3:Dic3)432,505
C6.16(C2×C3⋊Dic3) = C63.C2φ: C2×C3⋊Dic3/C62 → C2 ⊆ Aut C6216C6.16(C2xC3:Dic3)432,511
C6.17(C2×C3⋊Dic3) = C2×He3⋊4C8central extension (φ=1)144C6.17(C2xC3:Dic3)432,184
C6.18(C2×C3⋊Dic3) = C4×He3⋊3C4central extension (φ=1)144C6.18(C2xC3:Dic3)432,186
C6.19(C2×C3⋊Dic3) = C22×He3⋊3C4central extension (φ=1)144C6.19(C2xC3:Dic3)432,398
C6.20(C2×C3⋊Dic3) = C6×C32⋊4C8central extension (φ=1)144C6.20(C2xC3:Dic3)432,485
C6.21(C2×C3⋊Dic3) = C3×C12.58D6central extension (φ=1)72C6.21(C2xC3:Dic3)432,486
C6.22(C2×C3⋊Dic3) = C12×C3⋊Dic3central extension (φ=1)144C6.22(C2xC3:Dic3)432,487
C6.23(C2×C3⋊Dic3) = C3×C12⋊Dic3central extension (φ=1)144C6.23(C2xC3:Dic3)432,489
C6.24(C2×C3⋊Dic3) = C3×C62⋊5C4central extension (φ=1)72C6.24(C2xC3:Dic3)432,495
C6.25(C2×C3⋊Dic3) = He3⋊8M4(2)central stem extension (φ=1)726C6.25(C2xC3:Dic3)432,185
C6.26(C2×C3⋊Dic3) = C62.30D6central stem extension (φ=1)144C6.26(C2xC3:Dic3)432,188
C6.27(C2×C3⋊Dic3) = C62⋊4Dic3central stem extension (φ=1)72C6.27(C2xC3:Dic3)432,199

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