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

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

		d	ρ	Label	ID
C₂×Q₈⋊He₃		144		C2xQ8:He3	432,336

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊He₃⋊₁C₂ = C₃²⋊₂GL₂(𝔽₃)	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	72	12+	Q8:He3:1C2	432,248
Q₈⋊He₃⋊₂C₂ = C₃²⋊₃GL₂(𝔽₃)	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	72	6	Q8:He3:2C2	432,258
Q₈⋊He₃⋊₃C₂ = C₆.(S₃×A₄)	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	72	12+	Q8:He3:3C2	432,269
Q₈⋊He₃⋊₄C₂ = Q₈⋊He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	72	12-	Q8:He3:4C2	432,270
Q₈⋊He₃⋊₅C₂ = C₄○D₄⋊He₃	φ: trivial image	72	6	Q8:He3:5C2	432,339

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊He₃.₁C₂ = C₃²⋊CSU₂(𝔽₃)	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	144	12-	Q8:He3.1C2	432,247
Q₈⋊He₃.₂C₂ = C₃²⋊₂CSU₂(𝔽₃)	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊He₃	144	6	Q8:He3.2C2	432,257

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