Extensions 1→N→G→Q→1 with N=C₂² and Q=Q₈×C₃²

Direct product G=N×Q with N=C₂² and Q=Q₈×C₃²

		d	ρ	Label	ID
Q₈×C₆²		288		Q8xC6^2	288,1020

Semidirect products G=N:Q with N=C₂² and Q=Q₈×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(Q₈×C₃²) = C₃×Q₈×A₄	φ: Q₈×C₃²/C₃×Q₈ → C₃ ⊆ Aut C₂²	72	6	C2^2:(Q8xC3^2)	288,982
C₂²⋊₂(Q₈×C₃²) = C₃²×C₂²⋊Q₈	φ: Q₈×C₃²/C₃×C₁₂ → C₂ ⊆ Aut C₂²	144		C2^2:2(Q8xC3^2)	288,819

Non-split extensions G=N.Q with N=C₂² and Q=Q₈×C₃²

extension	φ:Q→Aut N	d	Label	ID
C₂².(Q₈×C₃²) = C₃²×C₈.C₄	φ: Q₈×C₃²/C₃×C₁₂ → C₂ ⊆ Aut C₂²	144	C2^2.(Q8xC3^2)	288,326
C₂².₂(Q₈×C₃²) = C₃²×C₂.C₄²	central extension (φ=1)	288	C2^2.2(Q8xC3^2)	288,313
C₂².₃(Q₈×C₃²) = C₄⋊C₄×C₃×C₆	central extension (φ=1)	288	C2^2.3(Q8xC3^2)	288,813

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22 and Q=Q8×C32