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

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

		d	ρ	Label	ID
C₃×Q₁₆⋊S₃		96	4	C3xQ16:S3	288,689

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(Q₁₆⋊S₃) = Dic₁₂⋊S₃	φ: Q₁₆⋊S₃/C₈⋊S₃ → C₂ ⊆ Aut C₃	48	4	C3:1(Q16:S3)	288,449
C₃⋊₂(Q₁₆⋊S₃) = D₁₂.₄D₆	φ: Q₁₆⋊S₃/C₂₄⋊C₂ → C₂ ⊆ Aut C₃	48	4	C3:2(Q16:S3)	288,459
C₃⋊₃(Q₁₆⋊S₃) = D₁₂.₁₅D₆	φ: Q₁₆⋊S₃/Q₈⋊₂S₃ → C₂ ⊆ Aut C₃	48	8-	C3:3(Q16:S3)	288,599
C₃⋊₄(Q₁₆⋊S₃) = Dic₆.₁₀D₆	φ: Q₁₆⋊S₃/C₃⋊Q₁₆ → C₂ ⊆ Aut C₃	48	8+	C3:4(Q16:S3)	288,593
C₃⋊₅(Q₁₆⋊S₃) = C₂₄.₃₅D₆	φ: Q₁₆⋊S₃/C₃×Q₁₆ → C₂ ⊆ Aut C₃	144		C3:5(Q16:S3)	288,775
C₃⋊₆(Q₁₆⋊S₃) = Dic₆.₂₂D₆	φ: Q₁₆⋊S₃/S₃×Q₈ → C₂ ⊆ Aut C₃	48	8+	C3:6(Q16:S3)	288,596
C₃⋊₇(Q₁₆⋊S₃) = D₁₂.₁₁D₆	φ: Q₁₆⋊S₃/Q₈⋊₃S₃ → C₂ ⊆ Aut C₃	96	8-	C3:7(Q16:S3)	288,591

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(Q₁₆⋊S₃) = Q₁₆⋊D₉	φ: Q₁₆⋊S₃/C₃×Q₁₆ → C₂ ⊆ Aut C₃	144	4	C3.(Q16:S3)	288,128

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