Extensions 1→N→G→Q→1 with N=C₂×C₁₄ and Q=Dic₃

Direct product G=N×Q with N=C₂×C₁₄ and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₂×C₁₄		336		Dic3xC2xC14	336,192

Semidirect products G=N:Q with N=C₂×C₁₄ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₄)⋊₁Dic₃ = C₇×A₄⋊C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂×C₁₄	84	3	(C2xC14):1Dic3	336,117
(C₂×C₁₄)⋊₂Dic₃ = A₄⋊Dic₇	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂×C₁₄	84	6-	(C2xC14):2Dic3	336,120
(C₂×C₁₄)⋊₃Dic₃ = C₇×C₆.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	168		(C2xC14):3Dic3	336,89
(C₂×C₁₄)⋊₄Dic₃ = C₄₂.₃₈D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	168		(C2xC14):4Dic3	336,105
(C₂×C₁₄)⋊₅Dic₃ = C₂²×Dic₂₁	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	336		(C2xC14):5Dic3	336,202

Non-split extensions G=N.Q with N=C₂×C₁₄ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₄).₁Dic₃ = C₇×C₄.Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	168	2	(C2xC14).1Dic3	336,80
(C₂×C₁₄).₂Dic₃ = C₂×C₂₁⋊C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	336		(C2xC14).2Dic3	336,95
(C₂×C₁₄).₃Dic₃ = C₈₄.C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂×C₁₄	168	2	(C2xC14).3Dic3	336,96
(C₂×C₁₄).₄Dic₃ = C₁₄×C₃⋊C₈	central extension (φ=1)	336		(C2xC14).4Dic3	336,79

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁