# Extensions 1→N→G→Q→1 with N=He3 and Q=C3×C6

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

Semidirect products G=N:Q with N=He3 and Q=C3×C6
extensionφ:Q→Out NdρLabelID
He3⋊(C3×C6) = C3×C3≀S3φ: C3×C6/C3C6 ⊆ Out He327He3:(C3xC6)486,115
He32(C3×C6) = C6×C3≀C3φ: C3×C6/C6C3 ⊆ Out He354He3:2(C3xC6)486,210
He33(C3×C6) = C6×He3⋊C3φ: C3×C6/C6C3 ⊆ Out He3162He3:3(C3xC6)486,212
He34(C3×C6) = C2×He3⋊C32φ: C3×C6/C6C3 ⊆ Out He3549He3:4(C3xC6)486,217
He35(C3×C6) = C32×C32⋊C6φ: C3×C6/C32C2 ⊆ Out He354He3:5(C3xC6)486,222
He36(C3×C6) = C32×He3⋊C2φ: C3×C6/C32C2 ⊆ Out He381He3:6(C3xC6)486,230
He37(C3×C6) = C2×3+ 1+4φ: trivial image549He3:7(C3xC6)486,254

Non-split extensions G=N.Q with N=He3 and Q=C3×C6
extensionφ:Q→Out NdρLabelID
He3.1(C3×C6) = C3×He3.C6φ: C3×C6/C3C6 ⊆ Out He381He3.1(C3xC6)486,118
He3.2(C3×C6) = C3×He3.2C6φ: C3×C6/C3C6 ⊆ Out He381He3.2(C3xC6)486,121
He3.3(C3×C6) = C3≀S33C3φ: C3×C6/C3C6 ⊆ Out He3273He3.3(C3xC6)486,125
He3.4(C3×C6) = C3≀C3⋊C6φ: C3×C6/C3C6 ⊆ Out He3279He3.4(C3xC6)486,126
He3.5(C3×C6) = He3.C3⋊C6φ: C3×C6/C3C6 ⊆ Out He3279He3.5(C3xC6)486,128
He3.6(C3×C6) = He3.(C3×C6)φ: C3×C6/C3C6 ⊆ Out He3279He3.6(C3xC6)486,130
He3.7(C3×C6) = C3≀C3.C6φ: C3×C6/C3C6 ⊆ Out He3279He3.7(C3xC6)486,132
He3.8(C3×C6) = C6×He3.C3φ: C3×C6/C6C3 ⊆ Out He3162He3.8(C3xC6)486,211
He3.9(C3×C6) = C2×C9.He3φ: C3×C6/C6C3 ⊆ Out He3543He3.9(C3xC6)486,214
He3.10(C3×C6) = C2×C33⋊C32φ: C3×C6/C6C3 ⊆ Out He3549He3.10(C3xC6)486,215
He3.11(C3×C6) = C2×He3.C32φ: C3×C6/C6C3 ⊆ Out He3549He3.11(C3xC6)486,216
He3.12(C3×C6) = C2×C9.2He3φ: C3×C6/C6C3 ⊆ Out He3549He3.12(C3xC6)486,219
He3.13(C3×C6) = C3×He3.4C6φ: C3×C6/C32C2 ⊆ Out He381He3.13(C3xC6)486,235
He3.14(C3×C6) = 3+ 1+42C2φ: C3×C6/C32C2 ⊆ Out He3279He3.14(C3xC6)486,237
He3.15(C3×C6) = 3- 1+42C2φ: C3×C6/C32C2 ⊆ Out He3279He3.15(C3xC6)486,239
He3.16(C3×C6) = C6×C9○He3φ: trivial image162He3.16(C3xC6)486,253
He3.17(C3×C6) = C2×3- 1+4φ: trivial image549He3.17(C3xC6)486,255

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