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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(S₃×Q₁₆) = S₃×Dic₁₂	φ: S₃×Q₁₆/S₃×C₈ → C₂ ⊆ Aut C₃	96	4-	C3:1(S3xQ16)	288,447
C₃⋊₂(S₃×Q₁₆) = C₂₄.₂₃D₆	φ: S₃×Q₁₆/Dic₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(S3xQ16)	288,450
C₃⋊₃(S₃×Q₁₆) = Dic₆.₉D₆	φ: S₃×Q₁₆/C₃⋊Q₁₆ → C₂ ⊆ Aut C₃	48	8-	C3:3(S3xQ16)	288,592
C₃⋊₄(S₃×Q₁₆) = Q₁₆×C₃⋊S₃	φ: S₃×Q₁₆/C₃×Q₁₆ → C₂ ⊆ Aut C₃	144		C3:4(S3xQ16)	288,774
C₃⋊₅(S₃×Q₁₆) = S₃×C₃⋊Q₁₆	φ: S₃×Q₁₆/S₃×Q₈ → C₂ ⊆ Aut C₃	96	8-	C3:5(S3xQ16)	288,590

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(S₃×Q₁₆) = Q₁₆×D₉	φ: S₃×Q₁₆/C₃×Q₁₆ → C₂ ⊆ Aut C₃	144	4-	C3.(S3xQ16)	288,127

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁