Extensions 1→N→G→Q→1 with N=C₆ and Q=S₃²

Direct product G=N×Q with N=C₆ and Q=S₃²

		d	ρ	Label	ID
S₃²×C₆		24	4	S3^2xC6	216,170

Semidirect products G=N:Q with N=C₆ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁S₃² = C₂×S₃×C₃⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36		C6:1S3^2	216,171
C₆⋊₂S₃² = C₂×C₃²⋊₄D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6:2S3^2	216,172

Non-split extensions G=N.Q with N=C₆ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁S₃² = C₉⋊Dic₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72	4-	C6.1S3^2	216,26
C₆.₂S₃² = Dic₃×D₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72	4-	C6.2S3^2	216,27
C₆.₃S₃² = C₁₈.D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36	4+	C6.3S3^2	216,28
C₆.₄S₃² = C₃⋊D₃₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36	4+	C6.4S3^2	216,29
C₆.₅S₃² = S₃×Dic₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72	4-	C6.5S3^2	216,30
C₆.₆S₃² = D₆⋊D₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72	4-	C6.6S3^2	216,31
C₆.₇S₃² = C₉⋊D₁₂	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36	4+	C6.7S3^2	216,32
C₆.₈S₃² = C₂×S₃×D₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36	4+	C6.8S3^2	216,101
C₆.₉S₃² = S₃×C₃⋊Dic₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72		C6.9S3^2	216,124
C₆.₁₀S₃² = Dic₃×C₃⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72		C6.10S3^2	216,125
C₆.₁₁S₃² = C₃³⋊₈(C₂×C₄)	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36		C6.11S3^2	216,126
C₆.₁₂S₃² = C₃³⋊₆D₄	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72		C6.12S3^2	216,127
C₆.₁₃S₃² = C₃³⋊₇D₄	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36		C6.13S3^2	216,128
C₆.₁₄S₃² = C₃³⋊₈D₄	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	36		C6.14S3^2	216,129
C₆.₁₅S₃² = C₃³⋊₄Q₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₆	72		C6.15S3^2	216,130
C₆.₁₆S₃² = He₃⋊₂Q₈	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	72	6-	C6.16S3^2	216,33
C₆.₁₇S₃² = C₆.S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	36	6	C6.17S3^2	216,34
C₆.₁₈S₃² = He₃⋊₂D₄	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	36	6+	C6.18S3^2	216,35
C₆.₁₉S₃² = He₃⋊(C₂×C₄)	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	36	6-	C6.19S3^2	216,36
C₆.₂₀S₃² = He₃⋊₃D₄	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	36	6	C6.20S3^2	216,37
C₆.₂₁S₃² = C₂×C₃²⋊D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	18	6+	C6.21S3^2	216,102
C₆.₂₂S₃² = C₃³⋊₉(C₂×C₄)	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6.22S3^2	216,131
C₆.₂₃S₃² = C₃³⋊₉D₄	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6.23S3^2	216,132
C₆.₂₄S₃² = C₃³⋊₅Q₈	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6.24S3^2	216,133
C₆.₂₅S₃² = C₃×S₃×Dic₃	central extension (φ=1)	24	4	C6.25S3^2	216,119
C₆.₂₆S₃² = C₃×C₆.D₆	central extension (φ=1)	24	4	C6.26S3^2	216,120
C₆.₂₇S₃² = C₃×D₆⋊S₃	central extension (φ=1)	24	4	C6.27S3^2	216,121
C₆.₂₈S₃² = C₃×C₃⋊D₁₂	central extension (φ=1)	24	4	C6.28S3^2	216,122
C₆.₂₉S₃² = C₃×C₃²⋊₂Q₈	central extension (φ=1)	24	4	C6.29S3^2	216,123

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Extensions 1→N→G→Q→1 with N=C6 and Q=S32

Extensions 1→N→G→Q→1 with N=C₆ and Q=S₃²