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

Direct product G=N×Q with N=He3⋊C3 and Q=C6
dρLabelID
C6×He3⋊C3162C6xHe3:C3486,212

Semidirect products G=N:Q with N=He3⋊C3 and Q=C6
extensionφ:Q→Out NdρLabelID
He3⋊C31C6 = He3.(C3×S3)φ: C6/C1C6 ⊆ Out He3⋊C32718+He3:C3:1C6486,131
He3⋊C32C6 = He3⋊(C3×S3)φ: C6/C1C6 ⊆ Out He3⋊C32718+He3:C3:2C6486,178
He3⋊C33C6 = He3.(C3×C6)φ: C6/C1C6 ⊆ Out He3⋊C3279He3:C3:3C6486,130
He3⋊C34C6 = C3≀C3.C6φ: C6/C1C6 ⊆ Out He3⋊C3279He3:C3:4C6486,132
He3⋊C35C6 = C2×C922C3φ: C6/C2C3 ⊆ Out He3⋊C3543He3:C3:5C6486,86
He3⋊C36C6 = C2×C32.He3φ: C6/C2C3 ⊆ Out He3⋊C3549He3:C3:6C6486,88
He3⋊C37C6 = C2×He3⋊C32φ: C6/C2C3 ⊆ Out He3⋊C3549He3:C3:7C6486,217
He3⋊C38C6 = C2×C9.2He3φ: C6/C2C3 ⊆ Out He3⋊C3549He3:C3:8C6486,219
He3⋊C39C6 = C3×He3.2C6φ: C6/C3C2 ⊆ Out He3⋊C381He3:C3:9C6486,121
He3⋊C310C6 = C3≀S33C3φ: C6/C3C2 ⊆ Out He3⋊C3273He3:C3:10C6486,125
He3⋊C311C6 = C3×He3.2S3φ: C6/C3C2 ⊆ Out He3⋊C3546He3:C3:11C6486,122
He3⋊C312C6 = C3×He3⋊S3φ: C6/C3C2 ⊆ Out He3⋊C3546He3:C3:12C6486,171
He3⋊C313C6 = C2×C9.He3φ: trivial image543He3:C3:13C6486,214

Non-split extensions G=N.Q with N=He3⋊C3 and Q=C6
extensionφ:Q→Out NdρLabelID
He3⋊C3.1C6 = C92⋊S3φ: C6/C1C6 ⊆ Out He3⋊C3276+He3:C3.1C6486,36
He3⋊C3.2C6 = C9⋊C9⋊S3φ: C6/C1C6 ⊆ Out He3⋊C32718+He3:C3.2C6486,41
He3⋊C3.3C6 = C2×C92⋊C3φ: C6/C2C3 ⊆ Out He3⋊C3543He3:C3.3C6486,85
He3⋊C3.4C6 = C2×C32.6He3φ: C6/C2C3 ⊆ Out He3⋊C3549He3:C3.4C6486,90

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