Extensions 1→N→G→Q→1 with N=C₃² and Q=He₃

Direct product G=N×Q with N=C₃² and Q=He₃

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

Semidirect products G=N:Q with N=C₃² and Q=He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊He₃ = C₃²⋊He₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27		C3^2:He3	243,37

Non-split extensions G=N.Q with N=C₃² and Q=He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁He₃ = C₉²⋊C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	3	C3^2.1He3	243,25
C₃².₂He₃ = C₉²⋊₂C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	3	C3^2.2He3	243,26
C₃².₃He₃ = C₉².C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	3	C3^2.3He3	243,27
C₃².₄He₃ = C₃².He₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.4He3	243,28
C₃².₅He₃ = C₃².₅He₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.5He3	243,29
C₃².₆He₃ = C₃².₆He₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.6He3	243,30
C₃².₇He₃ = C₃⁴.C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27		C3^2.7He3	243,38
C₃².₈He₃ = C₃².₂₃C₃³	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.8He3	243,40
C₃².₉He₃ = C₃×C₃≀C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27		C3^2.9He3	243,51
C₃².₁₀He₃ = C₃×He₃.C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.10He3	243,52
C₃².₁₁He₃ = C₃×He₃⋊C₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.11He3	243,53
C₃².₁₂He₃ = C₃×C₃.He₃	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.12He3	243,54
C₃².₁₃He₃ = C₃³⋊C₃²	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.13He3	243,56
C₃².₁₄He₃ = He₃.C₃²	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.14He3	243,57
C₃².₁₅He₃ = He₃⋊C₃²	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.15He3	243,58
C₃².₁₆He₃ = C₃².C₃³	φ: He₃/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.16He3	243,59
C₃².₁₇He₃ = C₃.C₉²	central extension (φ=1)	243		C3^2.17He3	243,2
C₃².₁₈He₃ = C₃³⋊C₉	central extension (φ=1)	27		C3^2.18He3	243,13
C₃².₁₉He₃ = C₃².₁₉He₃	central extension (φ=1)	81		C3^2.19He3	243,14
C₃².₂₀He₃ = C₃².₂₀He₃	central extension (φ=1)	81		C3^2.20He3	243,15
C₃².₂₁He₃ = He₃⋊C₉	central extension (φ=1)	81		C3^2.21He3	243,17
C₃².₂₂He₃ = 3_-¹⁺²⋊C₉	central extension (φ=1)	81		C3^2.22He3	243,18
C₃².₂₃He₃ = C₃×C₃²⋊C₉	central extension (φ=1)	81		C3^2.23He3	243,32
C₃².₂₄He₃ = C₃².₂₄He₃	central stem extension (φ=1)	81		C3^2.24He3	243,3
C₃².₂₅He₃ = C₃³.C₃²	central stem extension (φ=1)	81		C3^2.25He3	243,4
C₃².₂₆He₃ = C₃³.₃C₃²	central stem extension (φ=1)	81		C3^2.26He3	243,5
C₃².₂₇He₃ = C₃².₂₇He₃	central stem extension (φ=1)	81		C3^2.27He3	243,6
C₃².₂₈He₃ = C₃².₂₈He₃	central stem extension (φ=1)	81		C3^2.28He3	243,7
C₃².₂₉He₃ = C₃².₂₉He₃	central stem extension (φ=1)	81		C3^2.29He3	243,8
C₃².₃₀He₃ = C₃³.₇C₃²	central stem extension (φ=1)	81		C3^2.30He3	243,9

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Extensions 1→N→G→Q→1 with N=C32 and Q=He3

Extensions 1→N→G→Q→1 with N=C₃² and Q=He₃