# Extensions 1→N→G→Q→1 with N=C22 and Q=C22×C3⋊S3

Direct product G=N×Q with N=C22 and Q=C22×C3⋊S3
dρLabelID
C24×C3⋊S3144C2^4xC3:S3288,1044

Semidirect products G=N:Q with N=C22 and Q=C22×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C22⋊(C22×C3⋊S3) = C22×C3⋊S4φ: C22×C3⋊S3/C2×C6S3 ⊆ Aut C2236C2^2:(C2^2xC3:S3)288,1034
C222(C22×C3⋊S3) = C2×D4×C3⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C2272C2^2:2(C2^2xC3:S3)288,1007
C223(C22×C3⋊S3) = C22×C327D4φ: C22×C3⋊S3/C62C2 ⊆ Aut C22144C2^2:3(C2^2xC3:S3)288,1017

Non-split extensions G=N.Q with N=C22 and Q=C22×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C22.1(C22×C3⋊S3) = C2×C12.D6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C22144C2^2.1(C2^2xC3:S3)288,1008
C22.2(C22×C3⋊S3) = C4○D4×C3⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C2272C2^2.2(C2^2xC3:S3)288,1013
C22.3(C22×C3⋊S3) = C62.154C23φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C2272C2^2.3(C2^2xC3:S3)288,1014
C22.4(C22×C3⋊S3) = C3292- 1+4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C22144C2^2.4(C2^2xC3:S3)288,1015
C22.5(C22×C3⋊S3) = C2×C12.59D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C22144C2^2.5(C2^2xC3:S3)288,1006
C22.6(C22×C3⋊S3) = C3282+ 1+4φ: C22×C3⋊S3/C62C2 ⊆ Aut C2272C2^2.6(C2^2xC3:S3)288,1009
C22.7(C22×C3⋊S3) = C3272- 1+4φ: C22×C3⋊S3/C62C2 ⊆ Aut C22144C2^2.7(C2^2xC3:S3)288,1012
C22.8(C22×C3⋊S3) = C4×C324Q8central extension (φ=1)288C2^2.8(C2^2xC3:S3)288,725
C22.9(C22×C3⋊S3) = C42×C3⋊S3central extension (φ=1)144C2^2.9(C2^2xC3:S3)288,728
C22.10(C22×C3⋊S3) = C12216C2central extension (φ=1)144C2^2.10(C2^2xC3:S3)288,729
C22.11(C22×C3⋊S3) = C4×C12⋊S3central extension (φ=1)144C2^2.11(C2^2xC3:S3)288,730
C22.12(C22×C3⋊S3) = C62.221C23central extension (φ=1)144C2^2.12(C2^2xC3:S3)288,734
C22.13(C22×C3⋊S3) = C22⋊C4×C3⋊S3central extension (φ=1)72C2^2.13(C2^2xC3:S3)288,737
C22.14(C22×C3⋊S3) = C62.225C23central extension (φ=1)144C2^2.14(C2^2xC3:S3)288,738
C22.15(C22×C3⋊S3) = C62.231C23central extension (φ=1)288C2^2.15(C2^2xC3:S3)288,744
C22.16(C22×C3⋊S3) = C4⋊C4×C3⋊S3central extension (φ=1)144C2^2.16(C2^2xC3:S3)288,748
C22.17(C22×C3⋊S3) = C62.236C23central extension (φ=1)144C2^2.17(C2^2xC3:S3)288,749
C22.18(C22×C3⋊S3) = C62.237C23central extension (φ=1)144C2^2.18(C2^2xC3:S3)288,750
C22.19(C22×C3⋊S3) = C2×C4×C3⋊Dic3central extension (φ=1)288C2^2.19(C2^2xC3:S3)288,779
C22.20(C22×C3⋊S3) = C2×C6.Dic6central extension (φ=1)288C2^2.20(C2^2xC3:S3)288,780
C22.21(C22×C3⋊S3) = C2×C12⋊Dic3central extension (φ=1)288C2^2.21(C2^2xC3:S3)288,782
C22.22(C22×C3⋊S3) = C62.247C23central extension (φ=1)144C2^2.22(C2^2xC3:S3)288,783
C22.23(C22×C3⋊S3) = C2×C6.11D12central extension (φ=1)144C2^2.23(C2^2xC3:S3)288,784
C22.24(C22×C3⋊S3) = C4×C327D4central extension (φ=1)144C2^2.24(C2^2xC3:S3)288,785
C22.25(C22×C3⋊S3) = D4×C3⋊Dic3central extension (φ=1)144C2^2.25(C2^2xC3:S3)288,791
C22.26(C22×C3⋊S3) = Q8×C3⋊Dic3central extension (φ=1)288C2^2.26(C2^2xC3:S3)288,802
C22.27(C22×C3⋊S3) = C2×C625C4central extension (φ=1)144C2^2.27(C2^2xC3:S3)288,809
C22.28(C22×C3⋊S3) = C22×C324Q8central extension (φ=1)288C2^2.28(C2^2xC3:S3)288,1003
C22.29(C22×C3⋊S3) = C22×C4×C3⋊S3central extension (φ=1)144C2^2.29(C2^2xC3:S3)288,1004
C22.30(C22×C3⋊S3) = C22×C12⋊S3central extension (φ=1)144C2^2.30(C2^2xC3:S3)288,1005
C22.31(C22×C3⋊S3) = C2×Q8×C3⋊S3central extension (φ=1)144C2^2.31(C2^2xC3:S3)288,1010
C22.32(C22×C3⋊S3) = C2×C12.26D6central extension (φ=1)144C2^2.32(C2^2xC3:S3)288,1011
C22.33(C22×C3⋊S3) = C23×C3⋊Dic3central extension (φ=1)288C2^2.33(C2^2xC3:S3)288,1016
C22.34(C22×C3⋊S3) = C126Dic6central stem extension (φ=1)288C2^2.34(C2^2xC3:S3)288,726
C22.35(C22×C3⋊S3) = C12.25Dic6central stem extension (φ=1)288C2^2.35(C2^2xC3:S3)288,727
C22.36(C22×C3⋊S3) = C124D12central stem extension (φ=1)144C2^2.36(C2^2xC3:S3)288,731
C22.37(C22×C3⋊S3) = C1226C2central stem extension (φ=1)144C2^2.37(C2^2xC3:S3)288,732
C22.38(C22×C3⋊S3) = C1222C2central stem extension (φ=1)144C2^2.38(C2^2xC3:S3)288,733
C22.39(C22×C3⋊S3) = C626Q8central stem extension (φ=1)144C2^2.39(C2^2xC3:S3)288,735
C22.40(C22×C3⋊S3) = C62.223C23central stem extension (φ=1)144C2^2.40(C2^2xC3:S3)288,736
C22.41(C22×C3⋊S3) = C6212D4central stem extension (φ=1)72C2^2.41(C2^2xC3:S3)288,739
C22.42(C22×C3⋊S3) = C62.227C23central stem extension (φ=1)144C2^2.42(C2^2xC3:S3)288,740
C22.43(C22×C3⋊S3) = C62.228C23central stem extension (φ=1)144C2^2.43(C2^2xC3:S3)288,741
C22.44(C22×C3⋊S3) = C62.229C23central stem extension (φ=1)144C2^2.44(C2^2xC3:S3)288,742
C22.45(C22×C3⋊S3) = C62.69D4central stem extension (φ=1)144C2^2.45(C2^2xC3:S3)288,743
C22.46(C22×C3⋊S3) = C122Dic6central stem extension (φ=1)288C2^2.46(C2^2xC3:S3)288,745
C22.47(C22×C3⋊S3) = C62.233C23central stem extension (φ=1)288C2^2.47(C2^2xC3:S3)288,746
C22.48(C22×C3⋊S3) = C62.234C23central stem extension (φ=1)288C2^2.48(C2^2xC3:S3)288,747
C22.49(C22×C3⋊S3) = C62.238C23central stem extension (φ=1)144C2^2.49(C2^2xC3:S3)288,751
C22.50(C22×C3⋊S3) = C123D12central stem extension (φ=1)144C2^2.50(C2^2xC3:S3)288,752
C22.51(C22×C3⋊S3) = C62.240C23central stem extension (φ=1)144C2^2.51(C2^2xC3:S3)288,753
C22.52(C22×C3⋊S3) = C12.31D12central stem extension (φ=1)144C2^2.52(C2^2xC3:S3)288,754
C22.53(C22×C3⋊S3) = C62.242C23central stem extension (φ=1)144C2^2.53(C2^2xC3:S3)288,755
C22.54(C22×C3⋊S3) = C6210Q8central stem extension (φ=1)144C2^2.54(C2^2xC3:S3)288,781
C22.55(C22×C3⋊S3) = C62.129D4central stem extension (φ=1)144C2^2.55(C2^2xC3:S3)288,786
C22.56(C22×C3⋊S3) = C6219D4central stem extension (φ=1)144C2^2.56(C2^2xC3:S3)288,787
C22.57(C22×C3⋊S3) = C62.72D4central stem extension (φ=1)144C2^2.57(C2^2xC3:S3)288,792
C22.58(C22×C3⋊S3) = C62.254C23central stem extension (φ=1)144C2^2.58(C2^2xC3:S3)288,793
C22.59(C22×C3⋊S3) = C6213D4central stem extension (φ=1)72C2^2.59(C2^2xC3:S3)288,794
C22.60(C22×C3⋊S3) = C62.256C23central stem extension (φ=1)144C2^2.60(C2^2xC3:S3)288,795
C22.61(C22×C3⋊S3) = C6214D4central stem extension (φ=1)144C2^2.61(C2^2xC3:S3)288,796
C22.62(C22×C3⋊S3) = C62.258C23central stem extension (φ=1)144C2^2.62(C2^2xC3:S3)288,797
C22.63(C22×C3⋊S3) = C62.259C23central stem extension (φ=1)288C2^2.63(C2^2xC3:S3)288,801
C22.64(C22×C3⋊S3) = C62.261C23central stem extension (φ=1)144C2^2.64(C2^2xC3:S3)288,803
C22.65(C22×C3⋊S3) = C62.262C23central stem extension (φ=1)144C2^2.65(C2^2xC3:S3)288,804
C22.66(C22×C3⋊S3) = C6224D4central stem extension (φ=1)72C2^2.66(C2^2xC3:S3)288,810

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