Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=Dic₃

Direct product G=N×Q with N=C₂²×C₆ and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₂²×C₆		96		Dic3xC2^2xC6	288,1001

Semidirect products G=N:Q with N=C₂²×C₆ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊₁Dic₃ = C₆×A₄⋊C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72		(C2^2xC6):1Dic3	288,905
(C₂²×C₆)⋊₂Dic₃ = C₂×C₆.₇S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72		(C2^2xC6):2Dic3	288,916
(C₂²×C₆)⋊₃Dic₃ = C₃×C₂³.₇D₆	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	24	4	(C2^2xC6):3Dic3	288,268
(C₂²×C₆)⋊₄Dic₃ = C₆².₃₈D₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	72		(C2^2xC6):4Dic3	288,309
(C₂²×C₆)⋊₅Dic₃ = C₆×C₆.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6):5Dic3	288,723
(C₂²×C₆)⋊₆Dic₃ = C₂×C₆²⋊₅C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6):6Dic3	288,809
(C₂²×C₆)⋊₇Dic₃ = C₂³×C₃⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	288		(C2^2xC6):7Dic3	288,1016

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).₁Dic₃ = C₃×A₄⋊C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72	3	(C2^2xC6).1Dic3	288,398
(C₂²×C₆).₂Dic₃ = C₁₂.S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72	6	(C2^2xC6).2Dic3	288,68
(C₂²×C₆).₃Dic₃ = C₂×C₆.S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72		(C2^2xC6).3Dic3	288,341
(C₂²×C₆).₄Dic₃ = C₁₂.₁₂S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₆	72	6	(C2^2xC6).4Dic3	288,402
(C₂²×C₆).₅Dic₃ = C₃×C₁₂.D₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	24	4	(C2^2xC6).5Dic3	288,267
(C₂²×C₆).₆Dic₃ = C₃₆.D₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	72	4	(C2^2xC6).6Dic3	288,39
(C₂²×C₆).₇Dic₃ = C₂³⋊₂Dic₉	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	72	4	(C2^2xC6).7Dic3	288,41
(C₂²×C₆).₈Dic₃ = (C₆×D₄).S₃	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₆	72		(C2^2xC6).8Dic3	288,308
(C₂²×C₆).₉Dic₃ = C₃×C₁₂.₅₅D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6).9Dic3	288,264
(C₂²×C₆).₁₀Dic₃ = C₆×C₄.Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6).10Dic3	288,692
(C₂²×C₆).₁₁Dic₃ = C₃₆.₅₅D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).11Dic3	288,37
(C₂²×C₆).₁₂Dic₃ = C₂²×C₉⋊C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	288		(C2^2xC6).12Dic3	288,130
(C₂²×C₆).₁₃Dic₃ = C₂×C₄.Dic₉	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).13Dic3	288,131
(C₂²×C₆).₁₄Dic₃ = C₂×C₁₈.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).14Dic3	288,162
(C₂²×C₆).₁₅Dic₃ = C₆²⋊₇C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).15Dic3	288,305
(C₂²×C₆).₁₆Dic₃ = C₂³×Dic₉	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	288		(C2^2xC6).16Dic3	288,365
(C₂²×C₆).₁₇Dic₃ = C₂²×C₃²⋊₄C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	288		(C2^2xC6).17Dic3	288,777
(C₂²×C₆).₁₈Dic₃ = C₂×C₁₂.₅₈D₆	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).18Dic3	288,778
(C₂²×C₆).₁₉Dic₃ = C₂×C₆×C₃⋊C₈	central extension (φ=1)	96		(C2^2xC6).19Dic3	288,691

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁