Extensions 1→N→G→Q→1 with N=C₂³×C₆ and Q=C₆

Direct product G=N×Q with N=C₂³×C₆ and Q=C₆

		d	ρ	Label	ID
C₂³×C₆²		288		C2^3xC6^2	288,1045

Semidirect products G=N:Q with N=C₂³×C₆ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆)⋊₁C₆ = C₃×C₂⁴⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	24	6	(C2^3xC6):1C6	288,634
(C₂³×C₆)⋊₂C₆ = C₃×D₄×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36	6	(C2^3xC6):2C6	288,980
(C₂³×C₆)⋊₃C₆ = (C₂²×S₃)⋊A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	24	6	(C2^3xC6):3C6	288,411
(C₂³×C₆)⋊₄C₆ = A₄×C₃⋊D₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36	6	(C2^3xC6):4C6	288,928
(C₂³×C₆)⋊₅C₆ = C₂²×S₃×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36		(C2^3xC6):5C6	288,1037
(C₂³×C₆)⋊₆C₆ = S₃×C₂²⋊A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36		(C2^3xC6):6C6	288,1038
(C₂³×C₆)⋊₇C₆ = A₄×C₂²×C₆	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	72		(C2^3xC6):7C6	288,1041
(C₂³×C₆)⋊₈C₆ = C₆×C₂²⋊A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6):8C6	288,1042
(C₂³×C₆)⋊₉C₆ = C₃²×C₂²≀C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	72		(C2^3xC6):9C6	288,817
(C₂³×C₆)⋊₁₀C₆ = D₄×C₆²	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	144		(C2^3xC6):10C6	288,1019
(C₂³×C₆)⋊₁₁C₆ = C₃×C₂⁴⋊₄S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	24		(C2^3xC6):11C6	288,724
(C₂³×C₆)⋊₁₂C₆ = C₂×C₆×C₃⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	48		(C2^3xC6):12C6	288,1002
(C₂³×C₆)⋊₁₃C₆ = S₃×C₂³×C₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	96		(C2^3xC6):13C6	288,1043

Non-split extensions G=N.Q with N=C₂³×C₆ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆).₁C₆ = C₂⁴⋊C₁₈	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36	6	(C2^3xC6).1C6	288,73
(C₂³×C₆).₂C₆ = D₄×C₃.A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	36	6	(C2^3xC6).2C6	288,344
(C₂³×C₆).₃C₆ = C₂×Dic₃×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂³×C₆	72		(C2^3xC6).3C6	288,927
(C₂³×C₆).₄C₆ = C₂×C₄×C₃.A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	72		(C2^3xC6).4C6	288,343
(C₂³×C₆).₅C₆ = C₂³×C₃.A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	72		(C2^3xC6).5C6	288,837
(C₂³×C₆).₆C₆ = C₂×C₂⁴⋊C₉	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6).6C6	288,838
(C₂³×C₆).₇C₆ = A₄×C₂×C₁₂	φ: C₆/C₂ → C₃ ⊆ Aut C₂³×C₆	72		(C2^3xC6).7C6	288,979
(C₂³×C₆).₈C₆ = C₂²⋊C₄×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	144		(C2^3xC6).8C6	288,165
(C₂³×C₆).₉C₆ = C₉×C₂²≀C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	72		(C2^3xC6).9C6	288,170
(C₂³×C₆).₁₀C₆ = D₄×C₂×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	144		(C2^3xC6).10C6	288,368
(C₂³×C₆).₁₁C₆ = C₂²⋊C₄×C₃×C₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	144		(C2^3xC6).11C6	288,812
(C₂³×C₆).₁₂C₆ = C₆×C₆.D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	48		(C2^3xC6).12C6	288,723
(C₂³×C₆).₁₃C₆ = Dic₃×C₂²×C₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂³×C₆	96		(C2^3xC6).13C6	288,1001

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