Extensions 1→N→G→Q→1 with N=C₂²×C₁₄ and Q=S₃

Direct product G=N×Q with N=C₂²×C₁₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₂²×C₁₄		168		S3xC2^2xC14	336,226

Semidirect products G=N:Q with N=C₂²×C₁₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₄)⋊₁S₃ = C₁₄×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₄	42	3	(C2^2xC14):1S3	336,214
(C₂²×C₁₄)⋊₂S₃ = C₂×C₇⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₄	42	6+	(C2^2xC14):2S3	336,215
(C₂²×C₁₄)⋊₃S₃ = C₁₄×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	168		(C2^2xC14):3S3	336,193
(C₂²×C₁₄)⋊₄S₃ = C₂×C₂₁⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	168		(C2^2xC14):4S3	336,203
(C₂²×C₁₄)⋊₅S₃ = C₂³×D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	168		(C2^2xC14):5S3	336,227

Non-split extensions G=N.Q with N=C₂²×C₁₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₄).₁S₃ = C₇×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₄	84	3	(C2^2xC14).1S3	336,117
(C₂²×C₁₄).₂S₃ = A₄⋊Dic₇	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₄	84	6-	(C2^2xC14).2S3	336,120
(C₂²×C₁₄).₃S₃ = C₇×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	168		(C2^2xC14).3S3	336,89
(C₂²×C₁₄).₄S₃ = C₄₂.₃₈D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	168		(C2^2xC14).4S3	336,105
(C₂²×C₁₄).₅S₃ = C₂²×Dic₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₄	336		(C2^2xC14).5S3	336,202
(C₂²×C₁₄).₆S₃ = Dic₃×C₂×C₁₄	central extension (φ=1)	336		(C2^2xC14).6S3	336,192

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