Extensions 1→N→G→Q→1 with N=C₃×Q₁₆ and Q=S₃

Direct product G=N×Q with N=C₃×Q₁₆ and Q=S₃

		d	ρ	Label	ID
C₃×S₃×Q₁₆		96	4	C3xS3xQ16	288,688

Semidirect products G=N:Q with N=C₃×Q₁₆ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×Q₁₆)⋊₁S₃ = C₃²⋊₁₀SD₃₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144		(C3xQ16):1S3	288,303
(C₃×Q₁₆)⋊₂S₃ = Q₁₆×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144		(C3xQ16):2S3	288,774
(C₃×Q₁₆)⋊₃S₃ = C₂₄.₂₈D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144		(C3xQ16):3S3	288,776
(C₃×Q₁₆)⋊₄S₃ = C₂₄.₃₅D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144		(C3xQ16):4S3	288,775
(C₃×Q₁₆)⋊₅S₃ = C₃×C₈.₆D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	96	4	(C3xQ16):5S3	288,262
(C₃×Q₁₆)⋊₆S₃ = C₃×Q₁₆⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	96	4	(C3xQ16):6S3	288,689
(C₃×Q₁₆)⋊₇S₃ = C₃×D₂₄⋊C₂	φ: trivial image	96	4	(C3xQ16):7S3	288,690

Non-split extensions G=N.Q with N=C₃×Q₁₆ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×Q₁₆).₁S₃ = C₉⋊SD₃₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144	4+	(C3xQ16).1S3	288,35
(C₃×Q₁₆).₂S₃ = C₉⋊Q₃₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	288	4-	(C3xQ16).2S3	288,36
(C₃×Q₁₆).₃S₃ = Q₁₆×D₉	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144	4-	(C3xQ16).3S3	288,127
(C₃×Q₁₆).₄S₃ = D₇₂⋊₅C₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144	4+	(C3xQ16).4S3	288,129
(C₃×Q₁₆).₅S₃ = C₃²⋊₇Q₃₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	288		(C3xQ16).5S3	288,304
(C₃×Q₁₆).₆S₃ = Q₁₆⋊D₉	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	144	4	(C3xQ16).6S3	288,128
(C₃×Q₁₆).₇S₃ = C₃×C₃⋊Q₃₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×Q₁₆	96	4	(C3xQ16).7S3	288,263

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