# Extensions 1→N→G→Q→1 with N=He3 and Q=C2×C6

Direct product G=N×Q with N=He3 and Q=C2×C6
dρLabelID
C2×C6×He3108C2xC6xHe3324,152

Semidirect products G=N:Q with N=He3 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
He3⋊(C2×C6) = C2×C3≀S3φ: C2×C6/C2C6 ⊆ Out He3183He3:(C2xC6)324,68
He32(C2×C6) = C3×C32⋊D6φ: C2×C6/C3C22 ⊆ Out He3186He3:2(C2xC6)324,117
He33(C2×C6) = C22×C3≀C3φ: C2×C6/C22C3 ⊆ Out He336He3:3(C2xC6)324,86
He34(C2×C6) = C22×He3⋊C3φ: C2×C6/C22C3 ⊆ Out He3108He3:4(C2xC6)324,88
He35(C2×C6) = C6×C32⋊C6φ: C2×C6/C6C2 ⊆ Out He3366He3:5(C2xC6)324,138
He36(C2×C6) = C6×He3⋊C2φ: C2×C6/C6C2 ⊆ Out He354He3:6(C2xC6)324,145

Non-split extensions G=N.Q with N=He3 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
He3.1(C2×C6) = C2×He3.C6φ: C2×C6/C2C6 ⊆ Out He3543He3.1(C2xC6)324,70
He3.2(C2×C6) = C2×He3.2C6φ: C2×C6/C2C6 ⊆ Out He3543He3.2(C2xC6)324,72
He3.3(C2×C6) = C22×He3.C3φ: C2×C6/C22C3 ⊆ Out He3108He3.3(C2xC6)324,87
He3.4(C2×C6) = C2×He3.4C6φ: C2×C6/C6C2 ⊆ Out He3543He3.4(C2xC6)324,148
He3.5(C2×C6) = C22×C9○He3φ: trivial image108He3.5(C2xC6)324,154

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