Extensions 1→N→G→Q→1 with N=C₁₂₄ and Q=C₄

Direct product G=N×Q with N=C₁₂₄ and Q=C₄

		d	ρ	Label	ID
C₄×C₁₂₄		496		C4xC124	496,19

Semidirect products G=N:Q with N=C₁₂₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₄⋊₁C₄ = C₄⋊Dic₃₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124:1C4	496,12
C₁₂₄⋊₂C₄ = C₄×Dic₃₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124:2C4	496,10
C₁₂₄⋊₃C₄ = C₄⋊C₄×C₃₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124:3C4	496,21

Non-split extensions G=N.Q with N=C₁₂₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₄.₁C₄ = C₄.Dic₃₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.1C4	496,9
C₁₂₄.₂C₄ = C₃₁⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	496	2	C124.2C4	496,1
C₁₂₄.₃C₄ = C₂×C₃₁⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124.3C4	496,8
C₁₂₄.₄C₄ = M₄(2)×C₃₁	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.4C4	496,23

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