Extensions 1→N→G→Q→1 with N=C₃ and Q=C₄²⋊₄S₃

Direct product G=N×Q with N=C₃ and Q=C₄²⋊₄S₃

		d	ρ	Label	ID
C₃×C₄²⋊₄S₃		24	2	C3xC4^2:4S3	288,239

Semidirect products G=N:Q with N=C₃ and Q=C₄²⋊₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₄²⋊₄S₃) = C₁₂.₈₀D₁₂	φ: C₄²⋊₄S₃/C₄.Dic₃ → C₂ ⊆ Aut C₃	48	4	C3:1(C4^2:4S3)	288,218
C₃⋊₂(C₄²⋊₄S₃) = C₁₂²⋊C₂	φ: C₄²⋊₄S₃/C₄×C₁₂ → C₂ ⊆ Aut C₃	72		C3:2(C4^2:4S3)	288,280
C₃⋊₃(C₄²⋊₄S₃) = D₁₂⋊₂Dic₃	φ: C₄²⋊₄S₃/C₄○D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:3(C4^2:4S3)	288,217

Non-split extensions G=N.Q with N=C₃ and Q=C₄²⋊₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₄²⋊₄S₃) = C₄²⋊₄D₉	φ: C₄²⋊₄S₃/C₄×C₁₂ → C₂ ⊆ Aut C₃	72	2	C3.(C4^2:4S3)	288,12

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Extensions 1→N→G→Q→1 with N=C3 and Q=C42⋊4S3