Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=C₁₂

Direct product G=N×Q with N=C₃×C₆ and Q=C₁₂

		d	ρ	Label	ID
C₃×C₆×C₁₂		216		C3xC6xC12	216,150

Semidirect products G=N:Q with N=C₃×C₆ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊C₁₂ = C₂×C₃²⋊C₁₂	φ: C₁₂/C₂ → C₆ ⊆ Aut C₃×C₆	72		(C3xC6):C12	216,59
(C₃×C₆)⋊₂C₁₂ = C₆×C₃²⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃×C₆	24	4	(C3xC6):2C12	216,168
(C₃×C₆)⋊₃C₁₂ = C₂×C₄×He₃	φ: C₁₂/C₄ → C₃ ⊆ Aut C₃×C₆	72		(C3xC6):3C12	216,74
(C₃×C₆)⋊₄C₁₂ = Dic₃×C₃×C₆	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6):4C12	216,138
(C₃×C₆)⋊₅C₁₂ = C₆×C₃⋊Dic₃	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6):5C12	216,143

Non-split extensions G=N.Q with N=C₃×C₆ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).C₁₂ = He₃⋊₃C₈	φ: C₁₂/C₂ → C₆ ⊆ Aut C₃×C₆	72	6	(C3xC6).C12	216,14
(C₃×C₆).₂C₁₂ = C₃×C₃²⋊₂C₈	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃×C₆	24	4	(C3xC6).2C12	216,117
(C₃×C₆).₃C₁₂ = C₈×He₃	φ: C₁₂/C₄ → C₃ ⊆ Aut C₃×C₆	72	3	(C3xC6).3C12	216,19
(C₃×C₆).₄C₁₂ = C₈×3_-¹⁺²	φ: C₁₂/C₄ → C₃ ⊆ Aut C₃×C₆	72	3	(C3xC6).4C12	216,20
(C₃×C₆).₅C₁₂ = C₂×C₄×3_-¹⁺²	φ: C₁₂/C₄ → C₃ ⊆ Aut C₃×C₆	72		(C3xC6).5C12	216,75
(C₃×C₆).₆C₁₂ = C₉×C₃⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72	2	(C3xC6).6C12	216,13
(C₃×C₆).₇C₁₂ = Dic₃×C₁₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).7C12	216,56
(C₃×C₆).₈C₁₂ = C₃²×C₃⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).8C12	216,82
(C₃×C₆).₉C₁₂ = C₃×C₃²⋊₄C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).9C12	216,83

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