# Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C14

Direct product G=N×Q with N=C12 and Q=C2×C14
dρLabelID
C22×C84336C2^2xC84336,204

Semidirect products G=N:Q with N=C12 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
C12⋊(C2×C14) = S3×C7×D4φ: C2×C14/C7C22 ⊆ Aut C12844C12:(C2xC14)336,188
C122(C2×C14) = C14×D12φ: C2×C14/C14C2 ⊆ Aut C12168C12:2(C2xC14)336,186
C123(C2×C14) = S3×C2×C28φ: C2×C14/C14C2 ⊆ Aut C12168C12:3(C2xC14)336,185
C124(C2×C14) = D4×C42φ: C2×C14/C14C2 ⊆ Aut C12168C12:4(C2xC14)336,205

Non-split extensions G=N.Q with N=C12 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C14) = C7×D4⋊S3φ: C2×C14/C7C22 ⊆ Aut C121684C12.1(C2xC14)336,85
C12.2(C2×C14) = C7×D4.S3φ: C2×C14/C7C22 ⊆ Aut C121684C12.2(C2xC14)336,86
C12.3(C2×C14) = C7×Q82S3φ: C2×C14/C7C22 ⊆ Aut C121684C12.3(C2xC14)336,87
C12.4(C2×C14) = C7×C3⋊Q16φ: C2×C14/C7C22 ⊆ Aut C123364C12.4(C2xC14)336,88
C12.5(C2×C14) = C7×D42S3φ: C2×C14/C7C22 ⊆ Aut C121684C12.5(C2xC14)336,189
C12.6(C2×C14) = S3×C7×Q8φ: C2×C14/C7C22 ⊆ Aut C121684C12.6(C2xC14)336,190
C12.7(C2×C14) = C7×Q83S3φ: C2×C14/C7C22 ⊆ Aut C121684C12.7(C2xC14)336,191
C12.8(C2×C14) = C7×C24⋊C2φ: C2×C14/C14C2 ⊆ Aut C121682C12.8(C2xC14)336,76
C12.9(C2×C14) = C7×D24φ: C2×C14/C14C2 ⊆ Aut C121682C12.9(C2xC14)336,77
C12.10(C2×C14) = C7×Dic12φ: C2×C14/C14C2 ⊆ Aut C123362C12.10(C2xC14)336,78
C12.11(C2×C14) = C14×Dic6φ: C2×C14/C14C2 ⊆ Aut C12336C12.11(C2xC14)336,184
C12.12(C2×C14) = S3×C56φ: C2×C14/C14C2 ⊆ Aut C121682C12.12(C2xC14)336,74
C12.13(C2×C14) = C7×C8⋊S3φ: C2×C14/C14C2 ⊆ Aut C121682C12.13(C2xC14)336,75
C12.14(C2×C14) = C14×C3⋊C8φ: C2×C14/C14C2 ⊆ Aut C12336C12.14(C2xC14)336,79
C12.15(C2×C14) = C7×C4.Dic3φ: C2×C14/C14C2 ⊆ Aut C121682C12.15(C2xC14)336,80
C12.16(C2×C14) = C7×C4○D12φ: C2×C14/C14C2 ⊆ Aut C121682C12.16(C2xC14)336,187
C12.17(C2×C14) = D8×C21φ: C2×C14/C14C2 ⊆ Aut C121682C12.17(C2xC14)336,111
C12.18(C2×C14) = SD16×C21φ: C2×C14/C14C2 ⊆ Aut C121682C12.18(C2xC14)336,112
C12.19(C2×C14) = Q16×C21φ: C2×C14/C14C2 ⊆ Aut C123362C12.19(C2xC14)336,113
C12.20(C2×C14) = Q8×C42φ: C2×C14/C14C2 ⊆ Aut C12336C12.20(C2xC14)336,206
C12.21(C2×C14) = C4○D4×C21φ: C2×C14/C14C2 ⊆ Aut C121682C12.21(C2xC14)336,207
C12.22(C2×C14) = M4(2)×C21central extension (φ=1)1682C12.22(C2xC14)336,110

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