# Extensions 1→N→G→Q→1 with N=C12 and Q=C22×C6

Direct product G=N×Q with N=C12 and Q=C22×C6
dρLabelID
C22×C6×C12288C2^2xC6xC12288,1018

Semidirect products G=N:Q with N=C12 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C12⋊(C22×C6) = S3×C6×D4φ: C22×C6/C6C22 ⊆ Aut C1248C12:(C2^2xC6)288,992
C122(C22×C6) = C2×C6×D12φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12:2(C2^2xC6)288,990
C123(C22×C6) = S3×C22×C12φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12:3(C2^2xC6)288,989
C124(C22×C6) = D4×C62φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12:4(C2^2xC6)288,1019

Non-split extensions G=N.Q with N=C12 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C12.1(C22×C6) = C3×S3×D8φ: C22×C6/C6C22 ⊆ Aut C12484C12.1(C2^2xC6)288,681
C12.2(C22×C6) = C3×D8⋊S3φ: C22×C6/C6C22 ⊆ Aut C12484C12.2(C2^2xC6)288,682
C12.3(C22×C6) = C3×D83S3φ: C22×C6/C6C22 ⊆ Aut C12484C12.3(C2^2xC6)288,683
C12.4(C22×C6) = C3×S3×SD16φ: C22×C6/C6C22 ⊆ Aut C12484C12.4(C2^2xC6)288,684
C12.5(C22×C6) = C3×Q83D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.5(C2^2xC6)288,685
C12.6(C22×C6) = C3×D4.D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.6(C2^2xC6)288,686
C12.7(C22×C6) = C3×Q8.7D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.7(C2^2xC6)288,687
C12.8(C22×C6) = C3×S3×Q16φ: C22×C6/C6C22 ⊆ Aut C12964C12.8(C2^2xC6)288,688
C12.9(C22×C6) = C3×Q16⋊S3φ: C22×C6/C6C22 ⊆ Aut C12964C12.9(C2^2xC6)288,689
C12.10(C22×C6) = C3×D24⋊C2φ: C22×C6/C6C22 ⊆ Aut C12964C12.10(C2^2xC6)288,690
C12.11(C22×C6) = C6×D4⋊S3φ: C22×C6/C6C22 ⊆ Aut C1248C12.11(C2^2xC6)288,702
C12.12(C22×C6) = C3×D126C22φ: C22×C6/C6C22 ⊆ Aut C12244C12.12(C2^2xC6)288,703
C12.13(C22×C6) = C6×D4.S3φ: C22×C6/C6C22 ⊆ Aut C1248C12.13(C2^2xC6)288,704
C12.14(C22×C6) = C6×Q82S3φ: C22×C6/C6C22 ⊆ Aut C1296C12.14(C2^2xC6)288,712
C12.15(C22×C6) = C3×Q8.11D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.15(C2^2xC6)288,713
C12.16(C22×C6) = C6×C3⋊Q16φ: C22×C6/C6C22 ⊆ Aut C1296C12.16(C2^2xC6)288,714
C12.17(C22×C6) = C3×D4⋊D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.17(C2^2xC6)288,720
C12.18(C22×C6) = C3×Q8.13D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.18(C2^2xC6)288,721
C12.19(C22×C6) = C3×Q8.14D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.19(C2^2xC6)288,722
C12.20(C22×C6) = C6×D42S3φ: C22×C6/C6C22 ⊆ Aut C1248C12.20(C2^2xC6)288,993
C12.21(C22×C6) = C3×D46D6φ: C22×C6/C6C22 ⊆ Aut C12244C12.21(C2^2xC6)288,994
C12.22(C22×C6) = S3×C6×Q8φ: C22×C6/C6C22 ⊆ Aut C1296C12.22(C2^2xC6)288,995
C12.23(C22×C6) = C6×Q83S3φ: C22×C6/C6C22 ⊆ Aut C1296C12.23(C2^2xC6)288,996
C12.24(C22×C6) = C3×Q8.15D6φ: C22×C6/C6C22 ⊆ Aut C12484C12.24(C2^2xC6)288,997
C12.25(C22×C6) = C3×S3×C4○D4φ: C22×C6/C6C22 ⊆ Aut C12484C12.25(C2^2xC6)288,998
C12.26(C22×C6) = C3×D4○D12φ: C22×C6/C6C22 ⊆ Aut C12484C12.26(C2^2xC6)288,999
C12.27(C22×C6) = C3×Q8○D12φ: C22×C6/C6C22 ⊆ Aut C12484C12.27(C2^2xC6)288,1000
C12.28(C22×C6) = C6×C24⋊C2φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.28(C2^2xC6)288,673
C12.29(C22×C6) = C6×D24φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.29(C2^2xC6)288,674
C12.30(C22×C6) = C3×C4○D24φ: C22×C6/C2×C6C2 ⊆ Aut C12482C12.30(C2^2xC6)288,675
C12.31(C22×C6) = C6×Dic12φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.31(C2^2xC6)288,676
C12.32(C22×C6) = C3×C8⋊D6φ: C22×C6/C2×C6C2 ⊆ Aut C12484C12.32(C2^2xC6)288,679
C12.33(C22×C6) = C3×C8.D6φ: C22×C6/C2×C6C2 ⊆ Aut C12484C12.33(C2^2xC6)288,680
C12.34(C22×C6) = C2×C6×Dic6φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.34(C2^2xC6)288,988
C12.35(C22×C6) = S3×C2×C24φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.35(C2^2xC6)288,670
C12.36(C22×C6) = C6×C8⋊S3φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.36(C2^2xC6)288,671
C12.37(C22×C6) = C3×C8○D12φ: C22×C6/C2×C6C2 ⊆ Aut C12482C12.37(C2^2xC6)288,672
C12.38(C22×C6) = C3×S3×M4(2)φ: C22×C6/C2×C6C2 ⊆ Aut C12484C12.38(C2^2xC6)288,677
C12.39(C22×C6) = C3×D12.C4φ: C22×C6/C2×C6C2 ⊆ Aut C12484C12.39(C2^2xC6)288,678
C12.40(C22×C6) = C2×C6×C3⋊C8φ: C22×C6/C2×C6C2 ⊆ Aut C1296C12.40(C2^2xC6)288,691
C12.41(C22×C6) = C6×C4.Dic3φ: C22×C6/C2×C6C2 ⊆ Aut C1248C12.41(C2^2xC6)288,692
C12.42(C22×C6) = C3×D4.Dic3φ: C22×C6/C2×C6C2 ⊆ Aut C12484C12.42(C2^2xC6)288,719
C12.43(C22×C6) = C6×C4○D12φ: C22×C6/C2×C6C2 ⊆ Aut C1248C12.43(C2^2xC6)288,991
C12.44(C22×C6) = D8×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.44(C2^2xC6)288,182
C12.45(C22×C6) = SD16×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.45(C2^2xC6)288,183
C12.46(C22×C6) = Q16×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12288C12.46(C2^2xC6)288,184
C12.47(C22×C6) = C9×C4○D8φ: C22×C6/C2×C6C2 ⊆ Aut C121442C12.47(C2^2xC6)288,185
C12.48(C22×C6) = C9×C8⋊C22φ: C22×C6/C2×C6C2 ⊆ Aut C12724C12.48(C2^2xC6)288,186
C12.49(C22×C6) = C9×C8.C22φ: C22×C6/C2×C6C2 ⊆ Aut C121444C12.49(C2^2xC6)288,187
C12.50(C22×C6) = D4×C2×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.50(C2^2xC6)288,368
C12.51(C22×C6) = Q8×C2×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12288C12.51(C2^2xC6)288,369
C12.52(C22×C6) = C4○D4×C18φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.52(C2^2xC6)288,370
C12.53(C22×C6) = C9×2+ 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C12724C12.53(C2^2xC6)288,371
C12.54(C22×C6) = C9×2- 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C121444C12.54(C2^2xC6)288,372
C12.55(C22×C6) = D8×C3×C6φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.55(C2^2xC6)288,829
C12.56(C22×C6) = SD16×C3×C6φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.56(C2^2xC6)288,830
C12.57(C22×C6) = Q16×C3×C6φ: C22×C6/C2×C6C2 ⊆ Aut C12288C12.57(C2^2xC6)288,831
C12.58(C22×C6) = C32×C4○D8φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.58(C2^2xC6)288,832
C12.59(C22×C6) = C32×C8⋊C22φ: C22×C6/C2×C6C2 ⊆ Aut C1272C12.59(C2^2xC6)288,833
C12.60(C22×C6) = C32×C8.C22φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.60(C2^2xC6)288,834
C12.61(C22×C6) = Q8×C62φ: C22×C6/C2×C6C2 ⊆ Aut C12288C12.61(C2^2xC6)288,1020
C12.62(C22×C6) = C4○D4×C3×C6φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.62(C2^2xC6)288,1021
C12.63(C22×C6) = C32×2+ 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C1272C12.63(C2^2xC6)288,1022
C12.64(C22×C6) = C32×2- 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C12144C12.64(C2^2xC6)288,1023
C12.65(C22×C6) = M4(2)×C18central extension (φ=1)144C12.65(C2^2xC6)288,180
C12.66(C22×C6) = C9×C8○D4central extension (φ=1)1442C12.66(C2^2xC6)288,181
C12.67(C22×C6) = M4(2)×C3×C6central extension (φ=1)144C12.67(C2^2xC6)288,827
C12.68(C22×C6) = C32×C8○D4central extension (φ=1)144C12.68(C2^2xC6)288,828

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