Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₂²

Direct product G=N×Q with N=C₅₂ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₅₂		208		C2^2xC52	208,45

Semidirect products G=N:Q with N=C₅₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂⋊C₂² = D₄×D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	52	4+	C52:C2^2	208,39
C₅₂⋊₂C₂² = C₂×D₅₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104		C52:2C2^2	208,37
C₅₂⋊₃C₂² = C₂×C₄×D₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104		C52:3C2^2	208,36
C₅₂⋊₄C₂² = D₄×C₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104		C52:4C2^2	208,46

Non-split extensions G=N.Q with N=C₅₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁C₂² = D₄⋊D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4+	C52.1C2^2	208,15
C₅₂.₂C₂² = D₄.D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4-	C52.2C2^2	208,16
C₅₂.₃C₂² = Q₈⋊D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4+	C52.3C2^2	208,17
C₅₂.₄C₂² = C₁₃⋊Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	208	4-	C52.4C2^2	208,18
C₅₂.₅C₂² = D₄⋊₂D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4-	C52.5C2^2	208,40
C₅₂.₆C₂² = Q₈×D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4-	C52.6C2^2	208,41
C₅₂.₇C₂² = D₅₂⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₂	104	4+	C52.7C2^2	208,42
C₅₂.₈C₂² = C₁₀₄⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.8C2^2	208,6
C₅₂.₉C₂² = D₁₀₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2+	C52.9C2^2	208,7
C₅₂.₁₀C₂² = Dic₅₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	208	2-	C52.10C2^2	208,8
C₅₂.₁₁C₂² = C₂×Dic₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	208		C52.11C2^2	208,35
C₅₂.₁₂C₂² = C₈×D₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.12C2^2	208,4
C₅₂.₁₃C₂² = C₈⋊D₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.13C2^2	208,5
C₅₂.₁₄C₂² = C₂×C₁₃⋊₂C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	208		C52.14C2^2	208,9
C₅₂.₁₅C₂² = C₅₂.₄C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.15C2^2	208,10
C₅₂.₁₆C₂² = D₅₂⋊₅C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.16C2^2	208,38
C₅₂.₁₇C₂² = C₁₃×D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.17C2^2	208,25
C₅₂.₁₈C₂² = C₁₃×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.18C2^2	208,26
C₅₂.₁₉C₂² = C₁₃×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	208	2	C52.19C2^2	208,27
C₅₂.₂₀C₂² = Q₈×C₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	208		C52.20C2^2	208,47
C₅₂.₂₁C₂² = C₁₃×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.21C2^2	208,48
C₅₂.₂₂C₂² = C₁₃×M₄(2)	central extension (φ=1)	104	2	C52.22C2^2	208,24

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Extensions 1→N→G→Q→1 with N=C52 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₂²