Extensions 1→N→G→Q→1 with N=C₆² and Q=C₆

Direct product G=N×Q with N=C₆² and Q=C₆

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

Semidirect products G=N:Q with N=C₆² and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆²⋊₁C₆ = D₄×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36	6	C6^2:1C6	216,77
C₆²⋊₂C₆ = He₃⋊₆D₄	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36	6	C6^2:2C6	216,60
C₆²⋊₃C₆ = C₆²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	18	6+	C6^2:3C6	216,99
C₆²⋊₄C₆ = C₂²×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36		C6^2:4C6	216,110
C₆²⋊₅C₆ = C₃×S₃×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	24	6	C6^2:5C6	216,166
C₆²⋊₆C₆ = A₄×C₃⋊S₃	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36		C6^2:6C6	216,167
C₆²⋊₇C₆ = C₂×C₃²⋊A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	18	3	C6^2:7C6	216,107
C₆²⋊₈C₆ = C₂³×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	72		C6^2:8C6	216,115
C₆²⋊₉C₆ = A₄×C₃×C₆	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	54		C6^2:9C6	216,173
C₆²⋊₁₀C₆ = D₄×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	108		C6^2:10C6	216,151
C₆²⋊₁₁C₆ = C₃²×C₃⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	36		C6^2:11C6	216,139
C₆²⋊₁₂C₆ = C₃×C₃²⋊₇D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	36		C6^2:12C6	216,144
C₆²⋊₁₃C₆ = S₃×C₆²	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2:13C6	216,174
C₆²⋊₁₄C₆ = C₂×C₆×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2:14C6	216,175

Non-split extensions G=N.Q with N=C₆² and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆².₁C₆ = D₄×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36	6	C6^2.1C6	216,78
C₆².₂C₆ = C₂×C₃²⋊C₁₂	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	72		C6^2.2C6	216,59
C₆².₃C₆ = S₃×C₃.A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₆²	36	6	C6^2.3C6	216,98
C₆².₄C₆ = C₂×C₄×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	72		C6^2.4C6	216,74
C₆².₅C₆ = C₂×C₄×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	72		C6^2.5C6	216,75
C₆².₆C₆ = C₆×C₃.A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	54		C6^2.6C6	216,105
C₆².₇C₆ = C₂×C₃².A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	18	3	C6^2.7C6	216,106
C₆².₈C₆ = C₂³×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₆²	72		C6^2.8C6	216,116
C₆².₉C₆ = D₄×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	108		C6^2.9C6	216,76
C₆².₁₀C₆ = Dic₃×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.10C6	216,56
C₆².₁₁C₆ = C₉×C₃⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	36	2	C6^2.11C6	216,58
C₆².₁₂C₆ = S₃×C₂×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.12C6	216,109
C₆².₁₃C₆ = Dic₃×C₃×C₆	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.13C6	216,138
C₆².₁₄C₆ = C₆×C₃⋊Dic₃	φ: C₆/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.14C6	216,143

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