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

Direct product G=N×Q with N=C23 and Q=C23
dρLabelID
C2664C2^664,267

Semidirect products G=N:Q with N=C23 and Q=C23
extensionφ:Q→Aut NdρLabelID
C231C23 = C2×C22≀C2φ: C23/C2C22 ⊆ Aut C2316C2^3:1C2^364,202
C232C23 = C2×2+ 1+4φ: C23/C2C22 ⊆ Aut C2316C2^3:2C2^364,264
C233C23 = D4×C23φ: C23/C22C2 ⊆ Aut C2332C2^3:3C2^364,261

Non-split extensions G=N.Q with N=C23 and Q=C23
extensionφ:Q→Aut NdρLabelID
C23.1C23 = C2×C23⋊C4φ: C23/C2C22 ⊆ Aut C2316C2^3.1C2^364,90
C23.2C23 = C23.C23φ: C23/C2C22 ⊆ Aut C23164C2^3.2C2^364,91
C23.3C23 = C2≀C22φ: C23/C2C22 ⊆ Aut C2384+C2^3.3C2^364,138
C23.4C23 = C23.7D4φ: C23/C2C22 ⊆ Aut C23164C2^3.4C2^364,139
C23.5C23 = C2×C4⋊D4φ: C23/C2C22 ⊆ Aut C2332C2^3.5C2^364,203
C23.6C23 = C22.19C24φ: C23/C2C22 ⊆ Aut C2316C2^3.6C2^364,206
C23.7C23 = C2×C4.4D4φ: C23/C2C22 ⊆ Aut C2332C2^3.7C2^364,207
C23.8C23 = C2×C41D4φ: C23/C2C22 ⊆ Aut C2332C2^3.8C2^364,211
C23.9C23 = C22.26C24φ: C23/C2C22 ⊆ Aut C2332C2^3.9C2^364,213
C23.10C23 = C233D4φ: C23/C2C22 ⊆ Aut C2316C2^3.10C2^364,215
C23.11C23 = C22.29C24φ: C23/C2C22 ⊆ Aut C2316C2^3.11C2^364,216
C23.12C23 = C22.31C24φ: C23/C2C22 ⊆ Aut C2332C2^3.12C2^364,218
C23.13C23 = C22.32C24φ: C23/C2C22 ⊆ Aut C2316C2^3.13C2^364,219
C23.14C23 = C22.34C24φ: C23/C2C22 ⊆ Aut C2332C2^3.14C2^364,221
C23.15C23 = C22.35C24φ: C23/C2C22 ⊆ Aut C2332C2^3.15C2^364,222
C23.16C23 = C22.36C24φ: C23/C2C22 ⊆ Aut C2332C2^3.16C2^364,223
C23.17C23 = Q86D4φ: C23/C2C22 ⊆ Aut C2332C2^3.17C2^364,231
C23.18C23 = C22.45C24φ: C23/C2C22 ⊆ Aut C2316C2^3.18C2^364,232
C23.19C23 = C22.47C24φ: C23/C2C22 ⊆ Aut C2332C2^3.19C2^364,234
C23.20C23 = C22.49C24φ: C23/C2C22 ⊆ Aut C2332C2^3.20C2^364,236
C23.21C23 = C22.50C24φ: C23/C2C22 ⊆ Aut C2332C2^3.21C2^364,237
C23.22C23 = C22.53C24φ: C23/C2C22 ⊆ Aut C2332C2^3.22C2^364,240
C23.23C23 = C22.54C24φ: C23/C2C22 ⊆ Aut C2316C2^3.23C2^364,241
C23.24C23 = C24⋊C22φ: C23/C2C22 ⊆ Aut C2316C2^3.24C2^364,242
C23.25C23 = C22.56C24φ: C23/C2C22 ⊆ Aut C2332C2^3.25C2^364,243
C23.26C23 = C22.57C24φ: C23/C2C22 ⊆ Aut C2332C2^3.26C2^364,244
C23.27C23 = C2.C25φ: C23/C2C22 ⊆ Aut C23164C2^3.27C2^364,266
C23.28C23 = C2×C42⋊C2φ: C23/C22C2 ⊆ Aut C2332C2^3.28C2^364,195
C23.29C23 = C2×C4×D4φ: C23/C22C2 ⊆ Aut C2332C2^3.29C2^364,196
C23.30C23 = C4×C4○D4φ: C23/C22C2 ⊆ Aut C2332C2^3.30C2^364,198
C23.31C23 = C22.11C24φ: C23/C22C2 ⊆ Aut C2316C2^3.31C2^364,199
C23.32C23 = C23.32C23φ: C23/C22C2 ⊆ Aut C2332C2^3.32C2^364,200
C23.33C23 = C23.33C23φ: C23/C22C2 ⊆ Aut C2332C2^3.33C2^364,201
C23.34C23 = C2×C22⋊Q8φ: C23/C22C2 ⊆ Aut C2332C2^3.34C2^364,204
C23.35C23 = C2×C22.D4φ: C23/C22C2 ⊆ Aut C2332C2^3.35C2^364,205
C23.36C23 = C23.36C23φ: C23/C22C2 ⊆ Aut C2332C2^3.36C2^364,210
C23.37C23 = C23.37C23φ: C23/C22C2 ⊆ Aut C2332C2^3.37C2^364,214
C23.38C23 = C23.38C23φ: C23/C22C2 ⊆ Aut C2332C2^3.38C2^364,217
C23.39C23 = C22.33C24φ: C23/C22C2 ⊆ Aut C2332C2^3.39C2^364,220
C23.40C23 = C232Q8φ: C23/C22C2 ⊆ Aut C2316C2^3.40C2^364,224
C23.41C23 = C23.41C23φ: C23/C22C2 ⊆ Aut C2332C2^3.41C2^364,225
C23.42C23 = D42φ: C23/C22C2 ⊆ Aut C2316C2^3.42C2^364,226
C23.43C23 = D45D4φ: C23/C22C2 ⊆ Aut C2316C2^3.43C2^364,227
C23.44C23 = D46D4φ: C23/C22C2 ⊆ Aut C2332C2^3.44C2^364,228
C23.45C23 = Q85D4φ: C23/C22C2 ⊆ Aut C2332C2^3.45C2^364,229
C23.46C23 = D4×Q8φ: C23/C22C2 ⊆ Aut C2332C2^3.46C2^364,230
C23.47C23 = C22.46C24φ: C23/C22C2 ⊆ Aut C2332C2^3.47C2^364,233
C23.48C23 = D43Q8φ: C23/C22C2 ⊆ Aut C2332C2^3.48C2^364,235
C23.49C23 = C22×C4○D4φ: C23/C22C2 ⊆ Aut C2332C2^3.49C2^364,263
C23.50C23 = C2×2- 1+4φ: C23/C22C2 ⊆ Aut C2332C2^3.50C2^364,265
C23.51C23 = C2×C2.C42central extension (φ=1)64C2^3.51C2^364,56
C23.52C23 = C424C4central extension (φ=1)64C2^3.52C2^364,57
C23.53C23 = C4×C22⋊C4central extension (φ=1)32C2^3.53C2^364,58
C23.54C23 = C4×C4⋊C4central extension (φ=1)64C2^3.54C2^364,59
C23.55C23 = C243C4central extension (φ=1)16C2^3.55C2^364,60
C23.56C23 = C23.7Q8central extension (φ=1)32C2^3.56C2^364,61
C23.57C23 = C23.34D4central extension (φ=1)32C2^3.57C2^364,62
C23.58C23 = C428C4central extension (φ=1)64C2^3.58C2^364,63
C23.59C23 = C425C4central extension (φ=1)64C2^3.59C2^364,64
C23.60C23 = C429C4central extension (φ=1)64C2^3.60C2^364,65
C23.61C23 = C23.8Q8central extension (φ=1)32C2^3.61C2^364,66
C23.62C23 = C23.23D4central extension (φ=1)32C2^3.62C2^364,67
C23.63C23 = C23.63C23central extension (φ=1)64C2^3.63C2^364,68
C23.64C23 = C24.C22central extension (φ=1)32C2^3.64C2^364,69
C23.65C23 = C23.65C23central extension (φ=1)64C2^3.65C2^364,70
C23.66C23 = C24.3C22central extension (φ=1)32C2^3.66C2^364,71
C23.67C23 = C23.67C23central extension (φ=1)64C2^3.67C2^364,72
C23.68C23 = C22×C22⋊C4central extension (φ=1)32C2^3.68C2^364,193
C23.69C23 = C22×C4⋊C4central extension (φ=1)64C2^3.69C2^364,194
C23.70C23 = C2×C4×Q8central extension (φ=1)64C2^3.70C2^364,197
C23.71C23 = C2×C42.C2central extension (φ=1)64C2^3.71C2^364,208
C23.72C23 = C2×C422C2central extension (φ=1)32C2^3.72C2^364,209
C23.73C23 = C2×C4⋊Q8central extension (φ=1)64C2^3.73C2^364,212
C23.74C23 = Q8×C23central extension (φ=1)64C2^3.74C2^364,262
C23.75C23 = C232D4central stem extension (φ=1)32C2^3.75C2^364,73
C23.76C23 = C23⋊Q8central stem extension (φ=1)32C2^3.76C2^364,74
C23.77C23 = C23.10D4central stem extension (φ=1)32C2^3.77C2^364,75
C23.78C23 = C23.78C23central stem extension (φ=1)64C2^3.78C2^364,76
C23.79C23 = C23.Q8central stem extension (φ=1)32C2^3.79C2^364,77
C23.80C23 = C23.11D4central stem extension (φ=1)32C2^3.80C2^364,78
C23.81C23 = C23.81C23central stem extension (φ=1)64C2^3.81C2^364,79
C23.82C23 = C23.4Q8central stem extension (φ=1)32C2^3.82C2^364,80
C23.83C23 = C23.83C23central stem extension (φ=1)64C2^3.83C2^364,81
C23.84C23 = C23.84C23central stem extension (φ=1)64C2^3.84C2^364,82

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