Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃³⋊C₂

Direct product G=N×Q with N=Q₈ and Q=C₃³⋊C₂

		d	ρ	Label	ID
Q₈×C₃³⋊C₂		216		Q8xC3^3:C2	432,726

Semidirect products G=N:Q with N=Q₈ and Q=C₃³⋊C₂

extension	φ:Q→Out N	d	Label	ID
Q₈⋊(C₃³⋊C₂) = C₃²⋊₅GL₂(𝔽₃)	φ: C₃³⋊C₂/C₃² → S₃ ⊆ Out Q₈	72	Q8:(C3^3:C2)	432,620
Q₈⋊₂(C₃³⋊C₂) = C₃³⋊₂₇SD₁₆	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Out Q₈	216	Q8:2(C3^3:C2)	432,509
Q₈⋊₃(C₃³⋊C₂) = (Q₈×C₃³)⋊C₂	φ: trivial image	216	Q8:3(C3^3:C2)	432,727

Non-split extensions G=N.Q with N=Q₈ and Q=C₃³⋊C₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(C₃³⋊C₂) = C₃²⋊₄CSU₂(𝔽₃)	φ: C₃³⋊C₂/C₃² → S₃ ⊆ Out Q₈	144		Q8.(C3^3:C2)	432,619
Q₈.₂(C₃³⋊C₂) = C₃³⋊₁₅Q₁₆	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Out Q₈	432		Q8.2(C3^3:C2)	432,510

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Q8 and Q=C33⋊C2