Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=C₁₂

Direct product G=N×Q with N=C₂²×C₆ and Q=C₁₂

		d	ρ	Label	ID
C₂²×C₆×C₁₂		288		C2^2xC6xC12	288,1018

Semidirect products G=N:Q with N=C₂²×C₆ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊C₁₂ = C₂×Dic₃×A₄	φ: C₁₂/C₂ → C₆ ⊆ Aut C₂²×C₆	72		(C2^2xC6):C12	288,927
(C₂²×C₆)⋊₂C₁₂ = C₃²×C₂³⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	72		(C2^2xC6):2C12	288,317
(C₂²×C₆)⋊₃C₁₂ = C₃×C₂³.₇D₆	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	24	4	(C2^2xC6):3C12	288,268
(C₂²×C₆)⋊₄C₁₂ = A₄×C₂×C₁₂	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂²×C₆	72		(C2^2xC6):4C12	288,979
(C₂²×C₆)⋊₅C₁₂ = C₂²⋊C₄×C₃×C₆	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6):5C12	288,812
(C₂²×C₆)⋊₆C₁₂ = C₆×C₆.D₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6):6C12	288,723
(C₂²×C₆)⋊₇C₁₂ = Dic₃×C₂²×C₆	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	96		(C2^2xC6):7C12	288,1001

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).C₁₂ = A₄×C₃⋊C₈	φ: C₁₂/C₂ → C₆ ⊆ Aut C₂²×C₆	72	6	(C2^2xC6).C12	288,408
(C₂²×C₆).₂C₁₂ = C₉×C₂³⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	72	4	(C2^2xC6).2C12	288,49
(C₂²×C₆).₃C₁₂ = C₉×C₄.D₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	72	4	(C2^2xC6).3C12	288,50
(C₂²×C₆).₄C₁₂ = C₃²×C₄.D₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	72		(C2^2xC6).4C12	288,318
(C₂²×C₆).₅C₁₂ = C₃×C₁₂.D₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂²×C₆	24	4	(C2^2xC6).5C12	288,267
(C₂²×C₆).₆C₁₂ = C₈×C₃.A₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂²×C₆	72	3	(C2^2xC6).6C12	288,76
(C₂²×C₆).₇C₁₂ = C₂×C₄×C₃.A₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂²×C₆	72		(C2^2xC6).7C12	288,343
(C₂²×C₆).₈C₁₂ = A₄×C₂₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂²×C₆	72	3	(C2^2xC6).8C12	288,637
(C₂²×C₆).₉C₁₂ = C₉×C₂²⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).9C12	288,48
(C₂²×C₆).₁₀C₁₂ = C₂²⋊C₄×C₁₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).10C12	288,165
(C₂²×C₆).₁₁C₁₂ = M₄(2)×C₁₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).11C12	288,180
(C₂²×C₆).₁₂C₁₂ = C₃²×C₂²⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).12C12	288,316
(C₂²×C₆).₁₃C₁₂ = M₄(2)×C₃×C₆	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).13C12	288,827
(C₂²×C₆).₁₄C₁₂ = C₃×C₁₂.₅₅D₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6).14C12	288,264
(C₂²×C₆).₁₅C₁₂ = C₂×C₆×C₃⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	96		(C2^2xC6).15C12	288,691
(C₂²×C₆).₁₆C₁₂ = C₆×C₄.Dic₃	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂²×C₆	48		(C2^2xC6).16C12	288,692

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