Extensions 1→N→G→Q→1 with N=C₃×He₃ and Q=C₃

Direct product G=N×Q with N=C₃×He₃ and Q=C₃

		d	ρ	Label	ID
C₃²×He₃		81		C3^2xHe3	243,62

Semidirect products G=N:Q with N=C₃×He₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×He₃)⋊₁C₃ = C₃².₂₄He₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3):1C3	243,3
(C₃×He₃)⋊₂C₃ = C₃²⋊He₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27		(C3xHe3):2C3	243,37
(C₃×He₃)⋊₃C₃ = C₃×C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27		(C3xHe3):3C3	243,51
(C₃×He₃)⋊₄C₃ = C₃×He₃⋊C₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3):4C3	243,53
(C₃×He₃)⋊₅C₃ = C₃³⋊C₃²	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27	9	(C3xHe3):5C3	243,56
(C₃×He₃)⋊₆C₃ = He₃⋊C₃²	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27	9	(C3xHe3):6C3	243,58
(C₃×He₃)⋊₇C₃ = 3₊¹⁺⁴	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27	9	(C3xHe3):7C3	243,65

Non-split extensions G=N.Q with N=C₃×He₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×He₃).₁C₃ = C₃³.C₃²	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).1C3	243,4
(C₃×He₃).₂C₃ = C₃².₂₇He₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).2C3	243,6
(C₃×He₃).₃C₃ = He₃⋊C₉	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).3C3	243,17
(C₃×He₃).₄C₃ = C₉⋊He₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).4C3	243,39
(C₃×He₃).₅C₃ = C₃².₂₃C₃³	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).5C3	243,40
(C₃×He₃).₆C₃ = C₃×He₃.C₃	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	81		(C3xHe3).6C3	243,52
(C₃×He₃).₇C₃ = He₃.C₃²	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27	9	(C3xHe3).7C3	243,57
(C₃×He₃).₈C₃ = 3_-¹⁺⁴	φ: C₃/C₁ → C₃ ⊆ Out C₃×He₃	27	9	(C3xHe3).8C3	243,66
(C₃×He₃).₉C₃ = C₉×He₃	φ: trivial image	81		(C3xHe3).9C3	243,35
(C₃×He₃).₁₀C₃ = C₃×C₉○He₃	φ: trivial image	81		(C3xHe3).10C3	243,64

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