Extensions 1→N→G→Q→1 with N=C₄×C₅₂ and Q=C₂

Direct product G=N×Q with N=C₄×C₅₂ and Q=C₂

		d	ρ	Label	ID
C₂×C₄×C₅₂		416		C2xC4xC52	416,175

Semidirect products G=N:Q with N=C₄×C₅₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₅₂)⋊₁C₂ = C₄²⋊₂D₁₃	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):1C2	416,97
(C₄×C₅₂)⋊₂C₂ = C₁₃×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):2C2	416,178
(C₄×C₅₂)⋊₃C₂ = C₁₃×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):3C2	416,187
(C₄×C₅₂)⋊₄C₂ = C₄⋊D₅₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):4C2	416,95
(C₄×C₅₂)⋊₅C₂ = C₄.D₅₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):5C2	416,96
(C₄×C₅₂)⋊₆C₂ = D₅₂⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	104	2	(C4xC52):6C2	416,12
(C₄×C₅₂)⋊₇C₂ = C₄×D₅₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):7C2	416,94
(C₄×C₅₂)⋊₈C₂ = C₄²×D₁₃	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):8C2	416,92
(C₄×C₅₂)⋊₉C₂ = C₄²⋊D₁₃	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):9C2	416,93
(C₄×C₅₂)⋊₁₀C₂ = C₁₃×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	104	2	(C4xC52):10C2	416,54
(C₄×C₅₂)⋊₁₁C₂ = D₄×C₅₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):11C2	416,179
(C₄×C₅₂)⋊₁₂C₂ = C₁₃×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):12C2	416,185
(C₄×C₅₂)⋊₁₃C₂ = C₁₃×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	208		(C4xC52):13C2	416,188

Non-split extensions G=N.Q with N=C₄×C₅₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₅₂).₁C₂ = C₁₃×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).1C2	416,47
(C₄×C₅₂).₂C₂ = C₅₂⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).2C2	416,90
(C₄×C₅₂).₃C₂ = C₅₂.₆Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).3C2	416,91
(C₄×C₅₂).₄C₂ = C₅₂⋊₃C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).4C2	416,11
(C₄×C₅₂).₅C₂ = C₄×Dic₂₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).5C2	416,89
(C₄×C₅₂).₆C₂ = C₄×C₁₃⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).6C2	416,9
(C₄×C₅₂).₇C₂ = C₂₆.₇C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).7C2	416,10
(C₄×C₅₂).₈C₂ = C₁₃×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).8C2	416,55
(C₄×C₅₂).₉C₂ = Q₈×C₅₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).9C2	416,180
(C₄×C₅₂).₁₀C₂ = C₁₃×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).10C2	416,186
(C₄×C₅₂).₁₁C₂ = C₁₃×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₂	416		(C4xC52).11C2	416,189

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