# Extensions 1→N→G→Q→1 with N=He3 and Q=C3×S3

Direct product G=N×Q with N=He3 and Q=C3×S3
dρLabelID
C3×S3×He354C3xS3xHe3486,223

Semidirect products G=N:Q with N=He3 and Q=C3×S3
extensionφ:Q→Out NdρLabelID
He31(C3×S3) = C3×C33⋊C6φ: C3×S3/C3S3 ⊆ Out He3186He3:1(C3xS3)486,116
He32(C3×S3) = C3×C33⋊S3φ: C3×S3/C3S3 ⊆ Out He3186He3:2(C3xS3)486,165
He33(C3×S3) = C3×He3⋊S3φ: C3×S3/C3S3 ⊆ Out He3546He3:3(C3xS3)486,171
He34(C3×S3) = He3⋊(C3×S3)φ: C3×S3/C3S3 ⊆ Out He32718+He3:4(C3xS3)486,178
He35(C3×S3) = C345S3φ: C3×S3/C3C6 ⊆ Out He3186He3:5(C3xS3)486,166
He36(C3×S3) = S3×C3≀C3φ: C3×S3/S3C3 ⊆ Out He3186He3:6(C3xS3)486,117
He37(C3×S3) = S3×He3⋊C3φ: C3×S3/S3C3 ⊆ Out He3546He3:7(C3xS3)486,123
He38(C3×S3) = C3×He34S3φ: C3×S3/C32C2 ⊆ Out He354He3:8(C3xS3)486,229
He39(C3×S3) = 3+ 1+4⋊C2φ: C3×S3/C32C2 ⊆ Out He32718+He3:9(C3xS3)486,236
He310(C3×S3) = C3×He35S3φ: C3×S3/C32C2 ⊆ Out He354He3:10(C3xS3)486,243

Non-split extensions G=N.Q with N=He3 and Q=C3×S3
extensionφ:Q→Out NdρLabelID
He3.1(C3×S3) = C3×He3.S3φ: C3×S3/C3S3 ⊆ Out He3546He3.1(C3xS3)486,119
He3.2(C3×S3) = C3×He3.2S3φ: C3×S3/C3S3 ⊆ Out He3546He3.2(C3xS3)486,122
He3.3(C3×S3) = (C3×He3)⋊C6φ: C3×S3/C3S3 ⊆ Out He32718+He3.3(C3xS3)486,127
He3.4(C3×S3) = C9⋊S3⋊C32φ: C3×S3/C3S3 ⊆ Out He32718+He3.4(C3xS3)486,129
He3.5(C3×S3) = He3.(C3×S3)φ: C3×S3/C3S3 ⊆ Out He32718+He3.5(C3xS3)486,131
He3.6(C3×S3) = C3×He3.3S3φ: C3×S3/C3S3 ⊆ Out He3546He3.6(C3xS3)486,168
He3.7(C3×S3) = C33⋊(C3×S3)φ: C3×S3/C3S3 ⊆ Out He32718+He3.7(C3xS3)486,176
He3.8(C3×S3) = He3.C32C6φ: C3×S3/C3S3 ⊆ Out He32718+He3.8(C3xS3)486,177
He3.9(C3×S3) = He3.C3⋊S3φ: C3×S3/C3C6 ⊆ Out He3546He3.9(C3xS3)486,169
He3.10(C3×S3) = He3⋊C32S3φ: C3×S3/C3C6 ⊆ Out He3546He3.10(C3xS3)486,172
He3.11(C3×S3) = S3×He3.C3φ: C3×S3/S3C3 ⊆ Out He3546He3.11(C3xS3)486,120
He3.12(C3×S3) = C3×He3.4S3φ: C3×S3/C32C2 ⊆ Out He3546He3.12(C3xS3)486,234
He3.13(C3×S3) = 3- 1+4⋊C2φ: C3×S3/C32C2 ⊆ Out He32718+He3.13(C3xS3)486,238
He3.14(C3×S3) = C9○He34S3φ: C3×S3/C32C2 ⊆ Out He3546He3.14(C3xS3)486,246
He3.15(C3×S3) = S3×C9○He3φ: trivial image546He3.15(C3xS3)486,226

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