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Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C3⋊C8

Direct product G=N×Q with N=C6 and Q=C2×C3⋊C8
dρLabelID
C2×C6×C3⋊C896C2xC6xC3:C8288,691

Semidirect products G=N:Q with N=C6 and Q=C2×C3⋊C8
extensionφ:Q→Aut NdρLabelID
C6⋊1(C2×C3⋊C8) = C2×S3×C3⋊C8φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C696C6:1(C2xC3:C8)288,460
C6⋊2(C2×C3⋊C8) = C22×C32⋊4C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6:2(C2xC3:C8)288,777

Non-split extensions G=N.Q with N=C6 and Q=C2×C3⋊C8
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C3⋊C8) = S3×C3⋊C16φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C6964C6.1(C2xC3:C8)288,189
C6.2(C2×C3⋊C8) = C24.61D6φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C6964C6.2(C2xC3:C8)288,191
C6.3(C2×C3⋊C8) = Dic3×C3⋊C8φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C696C6.3(C2xC3:C8)288,200
C6.4(C2×C3⋊C8) = C12.77D12φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C696C6.4(C2xC3:C8)288,204
C6.5(C2×C3⋊C8) = C12.81D12φ: C2×C3⋊C8/C3⋊C8 → C2 ⊆ Aut C696C6.5(C2xC3:C8)288,219
C6.6(C2×C3⋊C8) = C4×C9⋊C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.6(C2xC3:C8)288,9
C6.7(C2×C3⋊C8) = C36⋊C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.7(C2xC3:C8)288,11
C6.8(C2×C3⋊C8) = C2×C9⋊C16φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.8(C2xC3:C8)288,18
C6.9(C2×C3⋊C8) = C36.C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C61442C6.9(C2xC3:C8)288,19
C6.10(C2×C3⋊C8) = C36.55D4φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6144C6.10(C2xC3:C8)288,37
C6.11(C2×C3⋊C8) = C22×C9⋊C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.11(C2xC3:C8)288,130
C6.12(C2×C3⋊C8) = C4×C32⋊4C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.12(C2xC3:C8)288,277
C6.13(C2×C3⋊C8) = C12.57D12φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.13(C2xC3:C8)288,279
C6.14(C2×C3⋊C8) = C2×C24.S3φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6288C6.14(C2xC3:C8)288,286
C6.15(C2×C3⋊C8) = C24.94D6φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6144C6.15(C2xC3:C8)288,287
C6.16(C2×C3⋊C8) = C62⋊7C8φ: C2×C3⋊C8/C2×C12 → C2 ⊆ Aut C6144C6.16(C2xC3:C8)288,305
C6.17(C2×C3⋊C8) = C12×C3⋊C8central extension (φ=1)96C6.17(C2xC3:C8)288,236
C6.18(C2×C3⋊C8) = C3×C12⋊C8central extension (φ=1)96C6.18(C2xC3:C8)288,238
C6.19(C2×C3⋊C8) = C6×C3⋊C16central extension (φ=1)96C6.19(C2xC3:C8)288,245
C6.20(C2×C3⋊C8) = C3×C12.C8central extension (φ=1)482C6.20(C2xC3:C8)288,246
C6.21(C2×C3⋊C8) = C3×C12.55D4central extension (φ=1)48C6.21(C2xC3:C8)288,264

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