Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₂³

Direct product G=N×Q with N=C₅₂ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₅₂		416		C2^3xC52	416,227

Semidirect products G=N:Q with N=C₅₂ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₅₂⋊C₂³ = C₂×D₄×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	C52:C2^3	416,216
C₅₂⋊₂C₂³ = C₂²×D₅₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	C52:2C2^3	416,214
C₅₂⋊₃C₂³ = C₂²×C₄×D₁₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	C52:3C2^3	416,213
C₅₂⋊₄C₂³ = D₄×C₂×C₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	C52:4C2^3	416,228

Non-split extensions G=N.Q with N=C₅₂ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁C₂³ = D₈×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4+	C52.1C2^3	416,131
C₅₂.₂C₂³ = D₈⋊D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.2C2^3	416,132
C₅₂.₃C₂³ = D₈⋊₃D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.3C2^3	416,133
C₅₂.₄C₂³ = SD₁₆×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.4C2^3	416,134
C₅₂.₅C₂³ = Q₈⋊D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4+	C52.5C2^3	416,135
C₅₂.₆C₂³ = D₄.D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.6C2^3	416,136
C₅₂.₇C₂³ = D₂₆.₆D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.7C2^3	416,137
C₅₂.₈C₂³ = Q₁₆×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.8C2^3	416,138
C₅₂.₉C₂³ = Q₁₆⋊D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.9C2^3	416,139
C₅₂.₁₀C₂³ = D₁₀₄⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4+	C52.10C2^3	416,140
C₅₂.₁₁C₂³ = C₂×D₄⋊D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.11C2^3	416,152
C₅₂.₁₂C₂³ = D₅₂⋊₆C₂²	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.12C2^3	416,153
C₅₂.₁₃C₂³ = C₂×D₄.D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.13C2^3	416,154
C₅₂.₁₄C₂³ = C₂×Q₈⋊D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.14C2^3	416,162
C₅₂.₁₅C₂³ = Q₈.D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.15C2^3	416,163
C₅₂.₁₆C₂³ = C₂×C₁₃⋊Q₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	416		C52.16C2^3	416,164
C₅₂.₁₇C₂³ = D₄⋊D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4+	C52.17C2^3	416,170
C₅₂.₁₈C₂³ = C₅₂.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.18C2^3	416,171
C₅₂.₁₉C₂³ = D₄.₉D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.19C2^3	416,172
C₅₂.₂₀C₂³ = C₂×D₄⋊₂D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.20C2^3	416,217
C₅₂.₂₁C₂³ = D₄⋊₆D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.21C2^3	416,218
C₅₂.₂₂C₂³ = C₂×Q₈×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.22C2^3	416,219
C₅₂.₂₃C₂³ = C₂×D₅₂⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208		C52.23C2^3	416,220
C₅₂.₂₄C₂³ = Q₈.₁₀D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.24C2^3	416,221
C₅₂.₂₅C₂³ = C₄○D₄×D₁₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.25C2^3	416,222
C₅₂.₂₆C₂³ = D₄⋊₈D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	104	4+	C52.26C2^3	416,223
C₅₂.₂₇C₂³ = D₄.₁₀D₂₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.27C2^3	416,224
C₅₂.₂₈C₂³ = C₂×C₁₀₄⋊C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.28C2^3	416,123
C₅₂.₂₉C₂³ = C₂×D₁₀₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.29C2^3	416,124
C₅₂.₃₀C₂³ = D₁₀₄⋊₇C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	2	C52.30C2^3	416,125
C₅₂.₃₁C₂³ = C₂×Dic₅₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	416		C52.31C2^3	416,126
C₅₂.₃₂C₂³ = C₈⋊D₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	104	4+	C52.32C2^3	416,129
C₅₂.₃₃C₂³ = C₈.D₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	4-	C52.33C2^3	416,130
C₅₂.₃₄C₂³ = C₂²×Dic₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	416		C52.34C2^3	416,212
C₅₂.₃₅C₂³ = C₂×C₈×D₁₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.35C2^3	416,120
C₅₂.₃₆C₂³ = C₂×C₈⋊D₁₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.36C2^3	416,121
C₅₂.₃₇C₂³ = D₅₂.₃C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	2	C52.37C2^3	416,122
C₅₂.₃₈C₂³ = M₄(2)×D₁₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.38C2^3	416,127
C₅₂.₃₉C₂³ = D₅₂.₂C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.39C2^3	416,128
C₅₂.₄₀C₂³ = C₂²×C₁₃⋊₂C₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	416		C52.40C2^3	416,141
C₅₂.₄₁C₂³ = C₂×C₅₂.₄C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.41C2^3	416,142
C₅₂.₄₂C₂³ = D₄.Dic₁₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.42C2^3	416,169
C₅₂.₄₃C₂³ = C₂×D₅₂⋊₅C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.43C2^3	416,215
C₅₂.₄₄C₂³ = D₈×C₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.44C2^3	416,193
C₅₂.₄₅C₂³ = SD₁₆×C₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208		C52.45C2^3	416,194
C₅₂.₄₆C₂³ = Q₁₆×C₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	416		C52.46C2^3	416,195
C₅₂.₄₇C₂³ = C₁₃×C₄○D₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	2	C52.47C2^3	416,196
C₅₂.₄₈C₂³ = C₁₃×C₈⋊C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.48C2^3	416,197
C₅₂.₄₉C₂³ = C₁₃×C₈.C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.49C2^3	416,198
C₅₂.₅₀C₂³ = Q₈×C₂×C₂₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	416		C52.50C2^3	416,229
C₅₂.₅₁C₂³ = C₁₃×2₊¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.51C2^3	416,231
C₅₂.₅₂C₂³ = C₁₃×2_-¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.52C2^3	416,232
C₅₂.₅₃C₂³ = M₄(2)×C₂₆	central extension (φ=1)	208		C52.53C2^3	416,191
C₅₂.₅₄C₂³ = C₁₃×C₈○D₄	central extension (φ=1)	208	2	C52.54C2^3	416,192
C₅₂.₅₅C₂³ = C₄○D₄×C₂₆	central extension (φ=1)	208		C52.55C2^3	416,230

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Extensions 1→N→G→Q→1 with N=C52 and Q=C23

Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₂³