Extensions 1→N→G→Q→1 with N=Q₈ and Q=He₃⋊C₂

Direct product G=N×Q with N=Q₈ and Q=He₃⋊C₂

		d	ρ	Label	ID
Q₈×He₃⋊C₂		72	6	Q8xHe3:C2	432,394

Semidirect products G=N:Q with N=Q₈ and Q=He₃⋊C₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊(He₃⋊C₂) = C₃²⋊₃GL₂(𝔽₃)	φ: He₃⋊C₂/C₃² → S₃ ⊆ Out Q₈	72	6	Q8:(He3:C2)	432,258
Q₈⋊₂(He₃⋊C₂) = He₃⋊₁₁SD₁₆	φ: He₃⋊C₂/He₃ → C₂ ⊆ Out Q₈	72	6	Q8:2(He3:C2)	432,196
Q₈⋊₃(He₃⋊C₂) = He₃⋊₅D₄⋊C₂	φ: trivial image	72	6	Q8:3(He3:C2)	432,395

Non-split extensions G=N.Q with N=Q₈ and Q=He₃⋊C₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(He₃⋊C₂) = C₃²⋊₂CSU₂(𝔽₃)	φ: He₃⋊C₂/C₃² → S₃ ⊆ Out Q₈	144	6	Q8.(He3:C2)	432,257
Q₈.₂(He₃⋊C₂) = He₃⋊₇Q₁₆	φ: He₃⋊C₂/He₃ → C₂ ⊆ Out Q₈	144	6	Q8.2(He3:C2)	432,197

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Extensions 1→N→G→Q→1 with N=Q8 and Q=He3⋊C2