Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=S₃

Direct product G=N×Q with N=C₂×C₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₂×C₄		24		S3xC2xC4	48,35

Semidirect products G=N:Q with N=C₂×C₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁S₃ = D₆⋊C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	24		(C2xC4):1S3	48,14
(C₂×C₄)⋊₂S₃ = C₂×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	24		(C2xC4):2S3	48,36
(C₂×C₄)⋊₃S₃ = C₄○D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	24	2	(C2xC4):3S3	48,37

Non-split extensions G=N.Q with N=C₂×C₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁S₃ = Dic₃⋊C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	48		(C2xC4).1S3	48,12
(C₂×C₄).₂S₃ = C₄.Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	24	2	(C2xC4).2S3	48,10
(C₂×C₄).₃S₃ = C₄⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	48		(C2xC4).3S3	48,13
(C₂×C₄).₄S₃ = C₂×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₄	48		(C2xC4).4S3	48,34
(C₂×C₄).₅S₃ = C₂×C₃⋊C₈	central extension (φ=1)	48		(C2xC4).5S3	48,9
(C₂×C₄).₆S₃ = C₄×Dic₃	central extension (φ=1)	48		(C2xC4).6S3	48,11

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁