Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=Dic₃

Direct product G=N×Q with N=C₃×C₆ and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₃×C₆		72		Dic3xC3xC6	216,138

Semidirect products G=N:Q with N=C₃×C₆ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊₁Dic₃ = C₂×C₃²⋊C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72		(C3xC6):1Dic3	216,59
(C₃×C₆)⋊₂Dic₃ = C₂×He₃⋊₃C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72		(C3xC6):2Dic3	216,71
(C₃×C₆)⋊₃Dic₃ = C₂×C₃³⋊C₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₃×C₆	24	4	(C3xC6):3Dic3	216,169
(C₃×C₆)⋊₄Dic₃ = C₆×C₃⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6):4Dic3	216,143
(C₃×C₆)⋊₅Dic₃ = C₂×C₃³⋊₅C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	216		(C3xC6):5Dic3	216,148

Non-split extensions G=N.Q with N=C₃×C₆ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).₁Dic₃ = He₃⋊₃C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72	6	(C3xC6).1Dic3	216,14
(C₃×C₆).₂Dic₃ = C₉⋊C₂₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72	6	(C3xC6).2Dic3	216,15
(C₃×C₆).₃Dic₃ = He₃⋊₄C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72	3	(C3xC6).3Dic3	216,17
(C₃×C₆).₄Dic₃ = C₂×C₉⋊C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₃×C₆	72		(C3xC6).4Dic3	216,61
(C₃×C₆).₅Dic₃ = C₃³⋊₄C₈	φ: Dic₃/C₃ → C₄ ⊆ Aut C₃×C₆	24	4	(C3xC6).5Dic3	216,118
(C₃×C₆).₆Dic₃ = C₃×C₉⋊C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	72	2	(C3xC6).6Dic3	216,12
(C₃×C₆).₇Dic₃ = C₃₆.S₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	216		(C3xC6).7Dic3	216,16
(C₃×C₆).₈Dic₃ = C₆×Dic₉	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).8Dic3	216,55
(C₃×C₆).₉Dic₃ = C₂×C₉⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	216		(C3xC6).9Dic3	216,69
(C₃×C₆).₁₀Dic₃ = C₃×C₃²⋊₄C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).10Dic3	216,83
(C₃×C₆).₁₁Dic₃ = C₃³⋊₇C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₃×C₆	216		(C3xC6).11Dic3	216,84
(C₃×C₆).₁₂Dic₃ = C₃²×C₃⋊C₈	central extension (φ=1)	72		(C3xC6).12Dic3	216,82

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