Extensions 1→N→G→Q→1 with N=C₃ and Q=Q₈.₁₃D₆

Direct product G=N×Q with N=C₃ and Q=Q₈.₁₃D₆

		d	ρ	Label	ID
C₃×Q₈.₁₃D₆		48	4	C3xQ8.13D6	288,721

Semidirect products G=N:Q with N=C₃ and Q=Q₈.₁₃D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(Q₈.₁₃D₆) = D₁₂.₂₇D₆	φ: Q₈.₁₃D₆/C₂×C₃⋊C₈ → C₂ ⊆ Aut C₃	48	4	C3:1(Q8.13D6)	288,477
C₃⋊₂(Q₈.₁₃D₆) = D₁₂.₂₂D₆	φ: Q₈.₁₃D₆/D₄⋊S₃ → C₂ ⊆ Aut C₃	48	8-	C3:2(Q8.13D6)	288,581
C₃⋊₃(Q₈.₁₃D₆) = Dic₆.₂₀D₆	φ: Q₈.₁₃D₆/D₄.S₃ → C₂ ⊆ Aut C₃	48	8+	C3:3(Q8.13D6)	288,583
C₃⋊₄(Q₈.₁₃D₆) = D₁₂.₁₂D₆	φ: Q₈.₁₃D₆/Q₈⋊₂S₃ → C₂ ⊆ Aut C₃	96	8-	C3:4(Q8.13D6)	288,595
C₃⋊₅(Q₈.₁₃D₆) = D₁₂.₁₃D₆	φ: Q₈.₁₃D₆/C₃⋊Q₁₆ → C₂ ⊆ Aut C₃	48	8+	C3:5(Q8.13D6)	288,597
C₃⋊₆(Q₈.₁₃D₆) = D₁₂.₃₀D₆	φ: Q₈.₁₃D₆/C₄○D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:6(Q8.13D6)	288,470
C₃⋊₇(Q₈.₁₃D₆) = C₆².₇₄D₄	φ: Q₈.₁₃D₆/C₃×C₄○D₄ → C₂ ⊆ Aut C₃	144		C3:7(Q8.13D6)	288,807

Non-split extensions G=N.Q with N=C₃ and Q=Q₈.₁₃D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(Q₈.₁₃D₆) = D₄.₉D₁₈	φ: Q₈.₁₃D₆/C₃×C₄○D₄ → C₂ ⊆ Aut C₃	144	4	C3.(Q8.13D6)	288,161

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