Extensions 1→N→G→Q→1 with N=C₃³ and Q=D₆

Direct product G=N×Q with N=C₃³ and Q=D₆

		d	ρ	Label	ID
S₃×C₃²×C₆		108		S3xC3^2xC6	324,172

Semidirect products G=N:Q with N=C₃³ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊₁D₆ = He₃⋊D₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	9	6+	C3^3:1D6	324,39
C₃³⋊₂D₆ = S₃×C₃²⋊C₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	12+	C3^3:2D6	324,116
C₃³⋊₃D₆ = C₃×C₃²⋊D₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	6	C3^3:3D6	324,117
C₃³⋊₄D₆ = He₃⋊₅D₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	12+	C3^3:4D6	324,121
C₃³⋊₅D₆ = S₃×He₃⋊C₂	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	6	C3^3:5D6	324,122
C₃³⋊₆D₆ = He₃⋊₆D₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	27		C3^3:6D6	324,124
C₃³⋊₇D₆ = C₂×C₃≀S₃	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	18	3	C3^3:7D6	324,68
C₃³⋊₈D₆ = C₂×C₃³⋊S₃	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	18	6+	C3^3:8D6	324,77
C₃³⋊₉D₆ = C₆×C₃²⋊C₆	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	36	6	C3^3:9D6	324,138
C₃³⋊₁₀D₆ = C₂×He₃⋊₄S₃	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	54		C3^3:10D6	324,144
C₃³⋊₁₁D₆ = C₆×He₃⋊C₂	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	54		C3^3:11D6	324,145
C₃³⋊₁₂D₆ = C₂×He₃⋊₅S₃	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	36	6	C3^3:12D6	324,150
C₃³⋊₁₃D₆ = C₃×S₃×C₃⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	36		C3^3:13D6	324,166
C₃³⋊₁₄D₆ = C₃×C₃²⋊₄D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	12	4	C3^3:14D6	324,167
C₃³⋊₁₅D₆ = S₃×C₃³⋊C₂	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	54		C3^3:15D6	324,168
C₃³⋊₁₆D₆ = C₃⋊S₃²	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	18		C3^3:16D6	324,169
C₃³⋊₁₇D₆ = C₃³⋊₁₇D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	36		C3^3:17D6	324,170
C₃³⋊₁₈D₆ = S₃²×C₃²	φ: D₆/S₃ → C₂ ⊆ Aut C₃³	36		C3^3:18D6	324,165
C₃³⋊₁₉D₆ = C₃⋊S₃×C₃×C₆	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	36		C3^3:19D6	324,173
C₃³⋊₂₀D₆ = C₆×C₃³⋊C₂	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	108		C3^3:20D6	324,174
C₃³⋊₂₁D₆ = C₂×C₃⁴⋊C₂	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	162		C3^3:21D6	324,175

Non-split extensions G=N.Q with N=C₃³ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³.₁D₆ = C₃²⋊D₁₈	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	12+	C3^3.1D6	324,37
C₃³.₂D₆ = S₃×C₉⋊C₆	φ: D₆/C₁ → D₆ ⊆ Aut C₃³	18	12+	C3^3.2D6	324,118
C₃³.₃D₆ = C₂×C₃²⋊D₉	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	54		C3^3.3D6	324,63
C₃³.₄D₆ = C₂×C₃²⋊₂D₉	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	36	6	C3^3.4D6	324,75
C₃³.₅D₆ = C₆×C₉⋊C₆	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	36	6	C3^3.5D6	324,140
C₃³.₆D₆ = C₂×C₃³.S₃	φ: D₆/C₂ → S₃ ⊆ Aut C₃³	54		C3^3.6D6	324,146
C₃³.₇D₆ = C₃×S₃×D₉	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	36	4	C3^3.7D6	324,114
C₃³.₈D₆ = D₉×C₃⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	54		C3^3.8D6	324,119
C₃³.₉D₆ = S₃×C₉⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	54		C3^3.9D6	324,120
C₃³.₁₀D₆ = C₃²⋊₅D₁₈	φ: D₆/C₃ → C₂² ⊆ Aut C₃³	36	4	C3^3.10D6	324,123
C₃³.₁₁D₆ = D₉×C₃×C₆	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	108		C3^3.11D6	324,136
C₃³.₁₂D₆ = C₆×C₉⋊S₃	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	108		C3^3.12D6	324,142
C₃³.₁₃D₆ = C₂×C₃²⋊₄D₉	φ: D₆/C₆ → C₂ ⊆ Aut C₃³	162		C3^3.13D6	324,149

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Extensions 1→N→G→Q→1 with N=C33 and Q=D6

Extensions 1→N→G→Q→1 with N=C₃³ and Q=D₆