# Extensions 1→N→G→Q→1 with N=C32 and Q=C2×He3

Direct product G=N×Q with N=C32 and Q=C2×He3
dρLabelID
C3×C6×He3162C3xC6xHe3486,251

Semidirect products G=N:Q with N=C32 and Q=C2×He3
extensionφ:Q→Aut NdρLabelID
C32⋊(C2×He3) = C34⋊C6φ: C2×He3/C32C6 ⊆ Aut C32186C3^2:(C2xHe3)486,102
C322(C2×He3) = C2×C32⋊He3φ: C2×He3/C3×C6C3 ⊆ Aut C3254C3^2:2(C2xHe3)486,196
C323(C2×He3) = C3×S3×He3φ: C2×He3/He3C2 ⊆ Aut C3254C3^2:3(C2xHe3)486,223
C324(C2×He3) = C3⋊S3×He3φ: C2×He3/He3C2 ⊆ Aut C3254C3^2:4(C2xHe3)486,231

Non-split extensions G=N.Q with N=C32 and Q=C2×He3
extensionφ:Q→Aut NdρLabelID
C32.1(C2×He3) = C2×C92⋊C3φ: C2×He3/C3×C6C3 ⊆ Aut C32543C3^2.1(C2xHe3)486,85
C32.2(C2×He3) = C2×C922C3φ: C2×He3/C3×C6C3 ⊆ Aut C32543C3^2.2(C2xHe3)486,86
C32.3(C2×He3) = C2×C92.C3φ: C2×He3/C3×C6C3 ⊆ Aut C32543C3^2.3(C2xHe3)486,87
C32.4(C2×He3) = C2×C32.He3φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.4(C2xHe3)486,88
C32.5(C2×He3) = C2×C32.5He3φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.5(C2xHe3)486,89
C32.6(C2×He3) = C2×C32.6He3φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.6(C2xHe3)486,90
C32.7(C2×He3) = C2×C34.C3φ: C2×He3/C3×C6C3 ⊆ Aut C3254C3^2.7(C2xHe3)486,197
C32.8(C2×He3) = C2×C32.23C33φ: C2×He3/C3×C6C3 ⊆ Aut C32162C3^2.8(C2xHe3)486,199
C32.9(C2×He3) = C2×C33⋊C32φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.9(C2xHe3)486,215
C32.10(C2×He3) = C2×He3.C32φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.10(C2xHe3)486,216
C32.11(C2×He3) = C2×He3⋊C32φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.11(C2xHe3)486,217
C32.12(C2×He3) = C2×C32.C33φ: C2×He3/C3×C6C3 ⊆ Aut C32549C3^2.12(C2xHe3)486,218
C32.13(C2×He3) = S3×C32⋊C9φ: C2×He3/He3C2 ⊆ Aut C3254C3^2.13(C2xHe3)486,95
C32.14(C2×He3) = S3×C3≀C3φ: C2×He3/He3C2 ⊆ Aut C32186C3^2.14(C2xHe3)486,117
C32.15(C2×He3) = S3×He3.C3φ: C2×He3/He3C2 ⊆ Aut C32546C3^2.15(C2xHe3)486,120
C32.16(C2×He3) = S3×He3⋊C3φ: C2×He3/He3C2 ⊆ Aut C32546C3^2.16(C2xHe3)486,123
C32.17(C2×He3) = S3×C3.He3φ: C2×He3/He3C2 ⊆ Aut C32546C3^2.17(C2xHe3)486,124
C32.18(C2×He3) = C2×C3.C92central extension (φ=1)486C3^2.18(C2xHe3)486,62
C32.19(C2×He3) = C2×C33⋊C9central extension (φ=1)54C3^2.19(C2xHe3)486,73
C32.20(C2×He3) = C2×C32.19He3central extension (φ=1)162C3^2.20(C2xHe3)486,74
C32.21(C2×He3) = C2×C32.20He3central extension (φ=1)162C3^2.21(C2xHe3)486,75
C32.22(C2×He3) = C2×He3⋊C9central extension (φ=1)162C3^2.22(C2xHe3)486,77
C32.23(C2×He3) = C2×3- 1+2⋊C9central extension (φ=1)162C3^2.23(C2xHe3)486,78
C32.24(C2×He3) = C6×C32⋊C9central extension (φ=1)162C3^2.24(C2xHe3)486,191
C32.25(C2×He3) = C6×C3≀C3central extension (φ=1)54C3^2.25(C2xHe3)486,210
C32.26(C2×He3) = C6×He3.C3central extension (φ=1)162C3^2.26(C2xHe3)486,211
C32.27(C2×He3) = C6×He3⋊C3central extension (φ=1)162C3^2.27(C2xHe3)486,212
C32.28(C2×He3) = C6×C3.He3central extension (φ=1)162C3^2.28(C2xHe3)486,213
C32.29(C2×He3) = C2×C32.24He3central stem extension (φ=1)162C3^2.29(C2xHe3)486,63
C32.30(C2×He3) = C2×C33.C32central stem extension (φ=1)162C3^2.30(C2xHe3)486,64
C32.31(C2×He3) = C2×C33.3C32central stem extension (φ=1)162C3^2.31(C2xHe3)486,65
C32.32(C2×He3) = C2×C32.27He3central stem extension (φ=1)162C3^2.32(C2xHe3)486,66
C32.33(C2×He3) = C2×C32.28He3central stem extension (φ=1)162C3^2.33(C2xHe3)486,67
C32.34(C2×He3) = C2×C32.29He3central stem extension (φ=1)162C3^2.34(C2xHe3)486,68
C32.35(C2×He3) = C2×C33.7C32central stem extension (φ=1)162C3^2.35(C2xHe3)486,69

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