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

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

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊C₆² = S₃×C₆²	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6:C6^2	216,174

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁C₆² = C₃²×Dic₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6.1C6^2	216,135
C₆.₂C₆² = S₃×C₃×C₁₂	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6.2C6^2	216,136
C₆.₃C₆² = C₃²×D₁₂	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6.3C6^2	216,137
C₆.₄C₆² = Dic₃×C₃×C₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6.4C6^2	216,138
C₆.₅C₆² = C₃²×C₃⋊D₄	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₆	36		C6.5C6^2	216,139
C₆.₆C₆² = C₂×C₄×He₃	central extension (φ=1)	72		C6.6C6^2	216,74
C₆.₇C₆² = C₂×C₄×3_-¹⁺²	central extension (φ=1)	72		C6.7C6^2	216,75
C₆.₈C₆² = D₄×C₃×C₉	central extension (φ=1)	108		C6.8C6^2	216,76
C₆.₉C₆² = Q₈×C₃×C₉	central extension (φ=1)	216		C6.9C6^2	216,79
C₆.₁₀C₆² = C₂³×He₃	central extension (φ=1)	72		C6.10C6^2	216,115
C₆.₁₁C₆² = C₂³×3_-¹⁺²	central extension (φ=1)	72		C6.11C6^2	216,116
C₆.₁₂C₆² = D₄×C₃³	central extension (φ=1)	108		C6.12C6^2	216,151
C₆.₁₃C₆² = Q₈×C₃³	central extension (φ=1)	216		C6.13C6^2	216,152
C₆.₁₄C₆² = D₄×He₃	central stem extension (φ=1)	36	6	C6.14C6^2	216,77
C₆.₁₅C₆² = D₄×3_-¹⁺²	central stem extension (φ=1)	36	6	C6.15C6^2	216,78
C₆.₁₆C₆² = Q₈×He₃	central stem extension (φ=1)	72	6	C6.16C6^2	216,80
C₆.₁₇C₆² = Q₈×3_-¹⁺²	central stem extension (φ=1)	72	6	C6.17C6^2	216,81

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