Extensions 1→N→G→Q→1 with N=C₁₂₃ and Q=C₄

Direct product G=N×Q with N=C₁₂₃ and Q=C₄

		d	ρ	Label	ID
C₄₉₂		492	1	C492	492,4

Semidirect products G=N:Q with N=C₁₂₃ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₃⋊₁C₄ = C₄₁⋊Dic₃	φ: C₄/C₁ → C₄ ⊆ Aut C₁₂₃	123	4	C123:1C4	492,6
C₁₂₃⋊₂C₄ = C₃×C₄₁⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₁₂₃	123	4	C123:2C4	492,5
C₁₂₃⋊₃C₄ = Dic₁₂₃	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₃	492	2-	C123:3C4	492,3
C₁₂₃⋊₄C₄ = C₃×Dic₄₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₃	492	2	C123:4C4	492,2
C₁₂₃⋊₅C₄ = Dic₃×C₄₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₃	492	2	C123:5C4	492,1

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