# Extensions 1→N→G→Q→1 with N=C12 and Q=C2×A4

Direct product G=N×Q with N=C12 and Q=C2×A4
dρLabelID
A4×C2×C1272A4xC2xC12288,979

Semidirect products G=N:Q with N=C12 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
C121(C2×A4) = A4×D12φ: C2×A4/A4C2 ⊆ Aut C12366+C12:1(C2xA4)288,920
C122(C2×A4) = C4×S3×A4φ: C2×A4/A4C2 ⊆ Aut C12366C12:2(C2xA4)288,919
C123(C2×A4) = C3×D4×A4φ: C2×A4/A4C2 ⊆ Aut C12366C12:3(C2xA4)288,980

Non-split extensions G=N.Q with N=C12 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
C12.1(C2×A4) = A4×Dic6φ: C2×A4/A4C2 ⊆ Aut C12726-C12.1(C2xA4)288,918
C12.2(C2×A4) = Dic6.A4φ: C2×A4/A4C2 ⊆ Aut C12724+C12.2(C2xA4)288,924
C12.3(C2×A4) = D12.A4φ: C2×A4/A4C2 ⊆ Aut C12484-C12.3(C2xA4)288,926
C12.4(C2×A4) = A4×C3⋊C8φ: C2×A4/A4C2 ⊆ Aut C12726C12.4(C2xA4)288,408
C12.5(C2×A4) = SL2(𝔽3).Dic3φ: C2×A4/A4C2 ⊆ Aut C12964C12.5(C2xA4)288,410
C12.6(C2×A4) = S3×C4.A4φ: C2×A4/A4C2 ⊆ Aut C12484C12.6(C2xA4)288,925
C12.7(C2×A4) = D4×C3.A4φ: C2×A4/A4C2 ⊆ Aut C12366C12.7(C2xA4)288,344
C12.8(C2×A4) = Q8×C3.A4φ: C2×A4/A4C2 ⊆ Aut C12726C12.8(C2xA4)288,346
C12.9(C2×A4) = 2+ 1+4⋊C9φ: C2×A4/A4C2 ⊆ Aut C12724C12.9(C2xA4)288,348
C12.10(C2×A4) = 2- 1+4⋊C9φ: C2×A4/A4C2 ⊆ Aut C121444C12.10(C2xA4)288,349
C12.11(C2×A4) = C3×Q8×A4φ: C2×A4/A4C2 ⊆ Aut C12726C12.11(C2xA4)288,982
C12.12(C2×A4) = C3×Q8.A4φ: C2×A4/A4C2 ⊆ Aut C12724C12.12(C2xA4)288,984
C12.13(C2×A4) = C3×D4.A4φ: C2×A4/A4C2 ⊆ Aut C12484C12.13(C2xA4)288,985
C12.14(C2×A4) = C8×C3.A4central extension (φ=1)723C12.14(C2xA4)288,76
C12.15(C2×A4) = Q8.C36central extension (φ=1)1442C12.15(C2xA4)288,77
C12.16(C2×A4) = C2×C4×C3.A4central extension (φ=1)72C12.16(C2xA4)288,343
C12.17(C2×A4) = C2×Q8.C18central extension (φ=1)144C12.17(C2xA4)288,347
C12.18(C2×A4) = A4×C24central extension (φ=1)723C12.18(C2xA4)288,637
C12.19(C2×A4) = C3×C8.A4central extension (φ=1)962C12.19(C2xA4)288,638
C12.20(C2×A4) = C6×C4.A4central extension (φ=1)96C12.20(C2xA4)288,983

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