Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=S₃

Direct product G=N×Q with N=C₂²×C₆ and Q=S₃

		d	ρ	Label	ID
S₃×C₂²×C₆		48		S3xC2^2xC6	144,195

Semidirect products G=N:Q with N=C₂²×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊₁S₃ = C₆×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	18	3	(C2^2xC6):1S3	144,188
(C₂²×C₆)⋊₂S₃ = C₂×C₃⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	18	6+	(C2^2xC6):2S3	144,189
(C₂²×C₆)⋊₃S₃ = C₆×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	24		(C2^2xC6):3S3	144,167
(C₂²×C₆)⋊₄S₃ = C₂×C₃²⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6):4S3	144,177
(C₂²×C₆)⋊₅S₃ = C₂³×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6):5S3	144,196

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).₁S₃ = C₃×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	36	3	(C2^2xC6).1S3	144,123
(C₂²×C₆).₂S₃ = C₆.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	36	6-	(C2^2xC6).2S3	144,33
(C₂²×C₆).₃S₃ = C₂×C₃.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	18	6+	(C2^2xC6).3S3	144,109
(C₂²×C₆).₄S₃ = C₆.₇S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₆	36	6-	(C2^2xC6).4S3	144,126
(C₂²×C₆).₅S₃ = C₃×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	24		(C2^2xC6).5S3	144,84
(C₂²×C₆).₆S₃ = C₁₈.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6).6S3	144,19
(C₂²×C₆).₇S₃ = C₂²×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).7S3	144,45
(C₂²×C₆).₈S₃ = C₂×C₉⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6).8S3	144,46
(C₂²×C₆).₉S₃ = C₆²⋊₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6).9S3	144,100
(C₂²×C₆).₁₀S₃ = C₂³×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	72		(C2^2xC6).10S3	144,112
(C₂²×C₆).₁₁S₃ = C₂²×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₆	144		(C2^2xC6).11S3	144,176
(C₂²×C₆).₁₂S₃ = Dic₃×C₂×C₆	central extension (φ=1)	48		(C2^2xC6).12S3	144,166

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