Extensions 1→N→G→Q→1 with N=C₆² and Q=S₃

Direct product G=N×Q with N=C₆² and Q=S₃

		d	ρ	Label	ID
S₃×C₆²		72		S3xC6^2	216,174

Semidirect products G=N:Q with N=C₆² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆²⋊₁S₃ = C₃²×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36		C6^2:1S3	216,163
C₆²⋊₂S₃ = He₃⋊₆D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36	6	C6^2:2S3	216,60
C₆²⋊₃S₃ = He₃⋊₇D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36	6	C6^2:3S3	216,72
C₆²⋊₄S₃ = C₆²⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	18	6+	C6^2:4S3	216,92
C₆²⋊₅S₃ = C₃²⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	18	3	C6^2:5S3	216,95
C₆²⋊₆S₃ = C₂²×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36		C6^2:6S3	216,110
C₆²⋊₇S₃ = C₂²×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36		C6^2:7S3	216,113
C₆²⋊₈S₃ = C₃×C₃⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	24	6	C6^2:8S3	216,164
C₆²⋊₉S₃ = C₃²⋊₄S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36		C6^2:9S3	216,165
C₆²⋊₁₀S₃ = C₃²×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	36		C6^2:10S3	216,139
C₆²⋊₁₁S₃ = C₃×C₃²⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	36		C6^2:11S3	216,144
C₆²⋊₁₂S₃ = C₃³⋊₁₅D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	108		C6^2:12S3	216,149
C₆²⋊₁₃S₃ = C₂×C₆×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	72		C6^2:13S3	216,175
C₆²⋊₁₄S₃ = C₂²×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	108		C6^2:14S3	216,176

Non-split extensions G=N.Q with N=C₆² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆².₁S₃ = C₂×C₃²⋊C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	72		C6^2.1S3	216,59
C₆².₂S₃ = C₂×C₉⋊C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	72		C6^2.2S3	216,61
C₆².₃S₃ = Dic₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36	6	C6^2.3S3	216,62
C₆².₄S₃ = C₂×He₃⋊₃C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	72		C6^2.4S3	216,71
C₆².₅S₃ = C₃².S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	18	6+	C6^2.5S3	216,90
C₆².₆S₃ = C₃×C₃.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36	6	C6^2.6S3	216,91
C₆².₇S₃ = C₃².₃S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	54		C6^2.7S3	216,94
C₆².₈S₃ = C₂²×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₆²	36		C6^2.8S3	216,111
C₆².₉S₃ = C₆×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.9S3	216,55
C₆².₁₀S₃ = C₃×C₉⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	36	2	C6^2.10S3	216,57
C₆².₁₁S₃ = C₂×C₉⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	216		C6^2.11S3	216,69
C₆².₁₂S₃ = C₆.D₁₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	108		C6^2.12S3	216,70
C₆².₁₃S₃ = C₂×C₆×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.13S3	216,108
C₆².₁₄S₃ = C₂²×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	108		C6^2.14S3	216,112
C₆².₁₅S₃ = C₆×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	72		C6^2.15S3	216,143
C₆².₁₆S₃ = C₂×C₃³⋊₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆²	216		C6^2.16S3	216,148
C₆².₁₇S₃ = Dic₃×C₃×C₆	central extension (φ=1)	72		C6^2.17S3	216,138

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