Extensions 1→N→G→Q→1 with N=C₂xC₃₄ and Q=S₃

Direct product G=NxQ with N=C₂xC₃₄ and Q=S₃

		d	ρ	Label	ID
S₃xC₂xC₃₄		204		S3xC2xC34	408,44

Semidirect products G=N:Q with N=C₂xC₃₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₃₄):₁S₃ = C₁₇xS₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂xC₃₄	68	3	(C2xC34):1S3	408,36
(C₂xC₃₄):₂S₃ = C₁₇:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂xC₃₄	68	6+	(C2xC34):2S3	408,37
(C₂xC₃₄):₃S₃ = C₁₇xC₃:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₃₄	204	2	(C2xC34):3S3	408,24
(C₂xC₃₄):₄S₃ = C₅₁:₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₃₄	204	2	(C2xC34):4S3	408,29
(C₂xC₃₄):₅S₃ = C₂²xD₅₁	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₃₄	204		(C2xC34):5S3	408,45

Non-split extensions G=N.Q with N=C₂xC₃₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₃₄).S₃ = C₂xDic₅₁	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₃₄	408		(C2xC34).S3	408,28
(C₂xC₃₄).₂S₃ = Dic₃xC₃₄	central extension (φ=1)	408		(C2xC34).2S3	408,23

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