Extensions 1→N→G→Q→1 with N=C₁₂₄ and Q=C₂²

Direct product G=N×Q with N=C₁₂₄ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₁₂₄		496		C2^2xC124	496,37

Semidirect products G=N:Q with N=C₁₂₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₄⋊C₂² = D₄×D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	124	4+	C124:C2^2	496,31
C₁₂₄⋊₂C₂² = C₂×D₁₂₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248		C124:2C2^2	496,29
C₁₂₄⋊₃C₂² = C₂×C₄×D₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248		C124:3C2^2	496,28
C₁₂₄⋊₄C₂² = D₄×C₆₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248		C124:4C2^2	496,38

Non-split extensions G=N.Q with N=C₁₂₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₄.₁C₂² = D₄⋊D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4+	C124.1C2^2	496,14
C₁₂₄.₂C₂² = D₄.D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4-	C124.2C2^2	496,15
C₁₂₄.₃C₂² = Q₈⋊D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4+	C124.3C2^2	496,16
C₁₂₄.₄C₂² = C₃₁⋊Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	496	4-	C124.4C2^2	496,17
C₁₂₄.₅C₂² = D₄⋊₂D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4-	C124.5C2^2	496,32
C₁₂₄.₆C₂² = Q₈×D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4-	C124.6C2^2	496,33
C₁₂₄.₇C₂² = Q₈⋊₂D₃₁	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₂₄	248	4+	C124.7C2^2	496,34
C₁₂₄.₈C₂² = C₂₄₈⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.8C2^2	496,5
C₁₂₄.₉C₂² = D₂₄₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2+	C124.9C2^2	496,6
C₁₂₄.₁₀C₂² = Dic₁₂₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	496	2-	C124.10C2^2	496,7
C₁₂₄.₁₁C₂² = C₂×Dic₆₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124.11C2^2	496,27
C₁₂₄.₁₂C₂² = C₈×D₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.12C2^2	496,3
C₁₂₄.₁₃C₂² = C₈⋊D₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.13C2^2	496,4
C₁₂₄.₁₄C₂² = C₂×C₃₁⋊C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124.14C2^2	496,8
C₁₂₄.₁₅C₂² = C₄.Dic₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.15C2^2	496,9
C₁₂₄.₁₆C₂² = D₁₂₄⋊₅C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.16C2^2	496,30
C₁₂₄.₁₇C₂² = D₈×C₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.17C2^2	496,24
C₁₂₄.₁₈C₂² = SD₁₆×C₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.18C2^2	496,25
C₁₂₄.₁₉C₂² = Q₁₆×C₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	496	2	C124.19C2^2	496,26
C₁₂₄.₂₀C₂² = Q₈×C₆₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	496		C124.20C2^2	496,39
C₁₂₄.₂₁C₂² = C₄○D₄×C₃₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₄	248	2	C124.21C2^2	496,40
C₁₂₄.₂₂C₂² = M₄(2)×C₃₁	central extension (φ=1)	248	2	C124.22C2^2	496,23

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Extensions 1→N→G→Q→1 with N=C124 and Q=C22

Extensions 1→N→G→Q→1 with N=C₁₂₄ and Q=C₂²