Extensions 1→N→G→Q→1 with N=He3⋊C2 and Q=C2×C4

Direct product G=N×Q with N=He3⋊C2 and Q=C2×C4
dρLabelID
C2×C4×He3⋊C272C2xC4xHe3:C2432,385

Semidirect products G=N:Q with N=He3⋊C2 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
He3⋊C21(C2×C4) = C4×C32⋊D6φ: C2×C4/C4C2 ⊆ Out He3⋊C2366He3:C2:1(C2xC4)432,300
He3⋊C22(C2×C4) = C22×He3⋊C4φ: C2×C4/C22C2 ⊆ Out He3⋊C272He3:C2:2(C2xC4)432,543
He3⋊C23(C2×C4) = C2×He3⋊(C2×C4)φ: C2×C4/C22C2 ⊆ Out He3⋊C272He3:C2:3(C2xC4)432,321

Non-split extensions G=N.Q with N=He3⋊C2 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
He3⋊C2.1(C2×C4) = C2×He3⋊C8φ: C2×C4/C2C4 ⊆ Out He3⋊C2546+He3:C2.1(C2xC4)432,529
He3⋊C2.2(C2×C4) = C2.SU3(𝔽2)φ: C2×C4/C2C22 ⊆ Out He3⋊C2723He3:C2.2(C2xC4)432,239
He3⋊C2.3(C2×C4) = C6.S3≀C2φ: C2×C4/C2C22 ⊆ Out He3⋊C2726-He3:C2.3(C2xC4)432,237
He3⋊C2.4(C2×C4) = C32⋊D6⋊C4φ: C2×C4/C2C22 ⊆ Out He3⋊C2366He3:C2.4(C2xC4)432,238
He3⋊C2.5(C2×C4) = C4×He3⋊C4φ: C2×C4/C4C2 ⊆ Out He3⋊C2723He3:C2.5(C2xC4)432,275

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