Extensions 1→N→G→Q→1 with N=C₂×C₃₈ and Q=S₃

Direct product G=N×Q with N=C₂×C₃₈ and Q=S₃

		d	ρ	Label	ID
S₃×C₂×C₃₈		228		S3xC2xC38	456,52

Semidirect products G=N:Q with N=C₂×C₃₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₃₈)⋊₁S₃ = C₁₉×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₃₈	76	3	(C2xC38):1S3	456,42
(C₂×C₃₈)⋊₂S₃ = C₁₉⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₃₈	76	6+	(C2xC38):2S3	456,43
(C₂×C₃₈)⋊₃S₃ = C₁₉×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₃₈	228	2	(C2xC38):3S3	456,33
(C₂×C₃₈)⋊₄S₃ = C₅₇⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₃₈	228	2	(C2xC38):4S3	456,38
(C₂×C₃₈)⋊₅S₃ = C₂²×D₅₇	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₃₈	228		(C2xC38):5S3	456,53

Non-split extensions G=N.Q with N=C₂×C₃₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₃₈).S₃ = C₂×Dic₅₇	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₃₈	456		(C2xC38).S3	456,37
(C₂×C₃₈).₂S₃ = Dic₃×C₃₈	central extension (φ=1)	456		(C2xC38).2S3	456,32

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