# Extensions 1→N→G→Q→1 with N=C22 and Q=S3×C2×C6

Direct product G=N×Q with N=C22 and Q=S3×C2×C6
dρLabelID
S3×C23×C696S3xC2^3xC6288,1043

Semidirect products G=N:Q with N=C22 and Q=S3×C2×C6
extensionφ:Q→Aut NdρLabelID
C22⋊(S3×C2×C6) = C2×C6×S4φ: S3×C2×C6/C2×C6S3 ⊆ Aut C2236C2^2:(S3xC2xC6)288,1033
C222(S3×C2×C6) = C22×S3×A4φ: S3×C2×C6/C22×S3C3 ⊆ Aut C2236C2^2:2(S3xC2xC6)288,1037
C223(S3×C2×C6) = S3×C6×D4φ: S3×C2×C6/S3×C6C2 ⊆ Aut C2248C2^2:3(S3xC2xC6)288,992
C224(S3×C2×C6) = C2×C6×C3⋊D4φ: S3×C2×C6/C62C2 ⊆ Aut C2248C2^2:4(S3xC2xC6)288,1002

Non-split extensions G=N.Q with N=C22 and Q=S3×C2×C6
extensionφ:Q→Aut NdρLabelID
C22.1(S3×C2×C6) = C6×D42S3φ: S3×C2×C6/S3×C6C2 ⊆ Aut C2248C2^2.1(S3xC2xC6)288,993
C22.2(S3×C2×C6) = C3×S3×C4○D4φ: S3×C2×C6/S3×C6C2 ⊆ Aut C22484C2^2.2(S3xC2xC6)288,998
C22.3(S3×C2×C6) = C3×D4○D12φ: S3×C2×C6/S3×C6C2 ⊆ Aut C22484C2^2.3(S3xC2xC6)288,999
C22.4(S3×C2×C6) = C3×Q8○D12φ: S3×C2×C6/S3×C6C2 ⊆ Aut C22484C2^2.4(S3xC2xC6)288,1000
C22.5(S3×C2×C6) = C6×C4○D12φ: S3×C2×C6/C62C2 ⊆ Aut C2248C2^2.5(S3xC2xC6)288,991
C22.6(S3×C2×C6) = C3×D46D6φ: S3×C2×C6/C62C2 ⊆ Aut C22244C2^2.6(S3xC2xC6)288,994
C22.7(S3×C2×C6) = C3×Q8.15D6φ: S3×C2×C6/C62C2 ⊆ Aut C22484C2^2.7(S3xC2xC6)288,997
C22.8(S3×C2×C6) = C12×Dic6central extension (φ=1)96C2^2.8(S3xC2xC6)288,639
C22.9(S3×C2×C6) = S3×C4×C12central extension (φ=1)96C2^2.9(S3xC2xC6)288,642
C22.10(S3×C2×C6) = C3×C422S3central extension (φ=1)96C2^2.10(S3xC2xC6)288,643
C22.11(S3×C2×C6) = C12×D12central extension (φ=1)96C2^2.11(S3xC2xC6)288,644
C22.12(S3×C2×C6) = C3×C23.16D6central extension (φ=1)48C2^2.12(S3xC2xC6)288,648
C22.13(S3×C2×C6) = C3×S3×C22⋊C4central extension (φ=1)48C2^2.13(S3xC2xC6)288,651
C22.14(S3×C2×C6) = C3×Dic34D4central extension (φ=1)48C2^2.14(S3xC2xC6)288,652
C22.15(S3×C2×C6) = C3×Dic6⋊C4central extension (φ=1)96C2^2.15(S3xC2xC6)288,658
C22.16(S3×C2×C6) = C3×S3×C4⋊C4central extension (φ=1)96C2^2.16(S3xC2xC6)288,662
C22.17(S3×C2×C6) = C3×C4⋊C47S3central extension (φ=1)96C2^2.17(S3xC2xC6)288,663
C22.18(S3×C2×C6) = C3×Dic35D4central extension (φ=1)96C2^2.18(S3xC2xC6)288,664
C22.19(S3×C2×C6) = Dic3×C2×C12central extension (φ=1)96C2^2.19(S3xC2xC6)288,693
C22.20(S3×C2×C6) = C6×Dic3⋊C4central extension (φ=1)96C2^2.20(S3xC2xC6)288,694
C22.21(S3×C2×C6) = C6×C4⋊Dic3central extension (φ=1)96C2^2.21(S3xC2xC6)288,696
C22.22(S3×C2×C6) = C3×C23.26D6central extension (φ=1)48C2^2.22(S3xC2xC6)288,697
C22.23(S3×C2×C6) = C6×D6⋊C4central extension (φ=1)96C2^2.23(S3xC2xC6)288,698
C22.24(S3×C2×C6) = C12×C3⋊D4central extension (φ=1)48C2^2.24(S3xC2xC6)288,699
C22.25(S3×C2×C6) = C3×D4×Dic3central extension (φ=1)48C2^2.25(S3xC2xC6)288,705
C22.26(S3×C2×C6) = C3×Q8×Dic3central extension (φ=1)96C2^2.26(S3xC2xC6)288,716
C22.27(S3×C2×C6) = C6×C6.D4central extension (φ=1)48C2^2.27(S3xC2xC6)288,723
C22.28(S3×C2×C6) = C2×C6×Dic6central extension (φ=1)96C2^2.28(S3xC2xC6)288,988
C22.29(S3×C2×C6) = S3×C22×C12central extension (φ=1)96C2^2.29(S3xC2xC6)288,989
C22.30(S3×C2×C6) = C2×C6×D12central extension (φ=1)96C2^2.30(S3xC2xC6)288,990
C22.31(S3×C2×C6) = S3×C6×Q8central extension (φ=1)96C2^2.31(S3xC2xC6)288,995
C22.32(S3×C2×C6) = C6×Q83S3central extension (φ=1)96C2^2.32(S3xC2xC6)288,996
C22.33(S3×C2×C6) = Dic3×C22×C6central extension (φ=1)96C2^2.33(S3xC2xC6)288,1001
C22.34(S3×C2×C6) = C3×C122Q8central stem extension (φ=1)96C2^2.34(S3xC2xC6)288,640
C22.35(S3×C2×C6) = C3×C12.6Q8central stem extension (φ=1)96C2^2.35(S3xC2xC6)288,641
C22.36(S3×C2×C6) = C3×C4⋊D12central stem extension (φ=1)96C2^2.36(S3xC2xC6)288,645
C22.37(S3×C2×C6) = C3×C427S3central stem extension (φ=1)96C2^2.37(S3xC2xC6)288,646
C22.38(S3×C2×C6) = C3×C423S3central stem extension (φ=1)96C2^2.38(S3xC2xC6)288,647
C22.39(S3×C2×C6) = C3×Dic3.D4central stem extension (φ=1)48C2^2.39(S3xC2xC6)288,649
C22.40(S3×C2×C6) = C3×C23.8D6central stem extension (φ=1)48C2^2.40(S3xC2xC6)288,650
C22.41(S3×C2×C6) = C3×D6⋊D4central stem extension (φ=1)48C2^2.41(S3xC2xC6)288,653
C22.42(S3×C2×C6) = C3×C23.9D6central stem extension (φ=1)48C2^2.42(S3xC2xC6)288,654
C22.43(S3×C2×C6) = C3×Dic3⋊D4central stem extension (φ=1)48C2^2.43(S3xC2xC6)288,655
C22.44(S3×C2×C6) = C3×C23.11D6central stem extension (φ=1)48C2^2.44(S3xC2xC6)288,656
C22.45(S3×C2×C6) = C3×C23.21D6central stem extension (φ=1)48C2^2.45(S3xC2xC6)288,657
C22.46(S3×C2×C6) = C3×C12⋊Q8central stem extension (φ=1)96C2^2.46(S3xC2xC6)288,659
C22.47(S3×C2×C6) = C3×Dic3.Q8central stem extension (φ=1)96C2^2.47(S3xC2xC6)288,660
C22.48(S3×C2×C6) = C3×C4.Dic6central stem extension (φ=1)96C2^2.48(S3xC2xC6)288,661
C22.49(S3×C2×C6) = C3×D6.D4central stem extension (φ=1)96C2^2.49(S3xC2xC6)288,665
C22.50(S3×C2×C6) = C3×C12⋊D4central stem extension (φ=1)96C2^2.50(S3xC2xC6)288,666
C22.51(S3×C2×C6) = C3×D6⋊Q8central stem extension (φ=1)96C2^2.51(S3xC2xC6)288,667
C22.52(S3×C2×C6) = C3×C4.D12central stem extension (φ=1)96C2^2.52(S3xC2xC6)288,668
C22.53(S3×C2×C6) = C3×C4⋊C4⋊S3central stem extension (φ=1)96C2^2.53(S3xC2xC6)288,669
C22.54(S3×C2×C6) = C3×C12.48D4central stem extension (φ=1)48C2^2.54(S3xC2xC6)288,695
C22.55(S3×C2×C6) = C3×C23.28D6central stem extension (φ=1)48C2^2.55(S3xC2xC6)288,700
C22.56(S3×C2×C6) = C3×C127D4central stem extension (φ=1)48C2^2.56(S3xC2xC6)288,701
C22.57(S3×C2×C6) = C3×C23.23D6central stem extension (φ=1)48C2^2.57(S3xC2xC6)288,706
C22.58(S3×C2×C6) = C3×C23.12D6central stem extension (φ=1)48C2^2.58(S3xC2xC6)288,707
C22.59(S3×C2×C6) = C3×C232D6central stem extension (φ=1)48C2^2.59(S3xC2xC6)288,708
C22.60(S3×C2×C6) = C3×D63D4central stem extension (φ=1)48C2^2.60(S3xC2xC6)288,709
C22.61(S3×C2×C6) = C3×C23.14D6central stem extension (φ=1)48C2^2.61(S3xC2xC6)288,710
C22.62(S3×C2×C6) = C3×C123D4central stem extension (φ=1)48C2^2.62(S3xC2xC6)288,711
C22.63(S3×C2×C6) = C3×Dic3⋊Q8central stem extension (φ=1)96C2^2.63(S3xC2xC6)288,715
C22.64(S3×C2×C6) = C3×D63Q8central stem extension (φ=1)96C2^2.64(S3xC2xC6)288,717
C22.65(S3×C2×C6) = C3×C12.23D4central stem extension (φ=1)96C2^2.65(S3xC2xC6)288,718
C22.66(S3×C2×C6) = C3×C244S3central stem extension (φ=1)24C2^2.66(S3xC2xC6)288,724

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