Extensions 1→N→G→Q→1 with N=C₄×C₁₉⋊C₃ and Q=C₂

Direct product G=N×Q with N=C₄×C₁₉⋊C₃ and Q=C₂

		d	ρ	Label	ID
C₂×C₄×C₁₉⋊C₃		152		C2xC4xC19:C3	456,19

Semidirect products G=N:Q with N=C₄×C₁₉⋊C₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×C₁₉⋊C₃)⋊₁C₂ = D₇₆⋊C₃	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	76	6+	(C4xC19:C3):1C2	456,9
(C₄×C₁₉⋊C₃)⋊₂C₂ = C₄×C₁₉⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	76	6	(C4xC19:C3):2C2	456,8
(C₄×C₁₉⋊C₃)⋊₃C₂ = D₄×C₁₉⋊C₃	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	76	6	(C4xC19:C3):3C2	456,20

Non-split extensions G=N.Q with N=C₄×C₁₉⋊C₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×C₁₉⋊C₃).₁C₂ = Dic₃₈⋊C₃	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	152	6-	(C4xC19:C3).1C2	456,7
(C₄×C₁₉⋊C₃).₂C₂ = C₁₉⋊C₂₄	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	152	6	(C4xC19:C3).2C2	456,1
(C₄×C₁₉⋊C₃).₃C₂ = Q₈×C₁₉⋊C₃	φ: C₂/C₁ → C₂ ⊆ Out C₄×C₁₉⋊C₃	152	6	(C4xC19:C3).3C2	456,21
(C₄×C₁₉⋊C₃).₄C₂ = C₈×C₁₉⋊C₃	φ: trivial image	152	3	(C4xC19:C3).4C2	456,2

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁