# Extensions 1→N→G→Q→1 with N=C23 and Q=D4

Direct product G=N×Q with N=C23 and Q=D4
dρLabelID
D4×C2332D4xC2^364,261

Semidirect products G=N:Q with N=C23 and Q=D4
extensionφ:Q→Aut NdρLabelID
C23⋊D4 = C2≀C22φ: D4/C1D4 ⊆ Aut C2384+C2^3:D464,138
C232D4 = C232D4φ: D4/C2C22 ⊆ Aut C2332C2^3:2D464,73
C233D4 = C233D4φ: D4/C2C22 ⊆ Aut C2316C2^3:3D464,215
C234D4 = C2×C4⋊D4φ: D4/C4C2 ⊆ Aut C2332C2^3:4D464,203
C235D4 = C2×C22≀C2φ: D4/C22C2 ⊆ Aut C2316C2^3:5D464,202

Non-split extensions G=N.Q with N=C23 and Q=D4
extensionφ:Q→Aut NdρLabelID
C23.1D4 = C2≀C4φ: D4/C1D4 ⊆ Aut C2384+C2^3.1D464,32
C23.2D4 = C23.D4φ: D4/C1D4 ⊆ Aut C23164C2^3.2D464,33
C23.3D4 = C42⋊C4φ: D4/C1D4 ⊆ Aut C2384+C2^3.3D464,34
C23.4D4 = C423C4φ: D4/C1D4 ⊆ Aut C23164C2^3.4D464,35
C23.5D4 = D44D4φ: D4/C1D4 ⊆ Aut C2384+C2^3.5D464,134
C23.6D4 = D4.9D4φ: D4/C1D4 ⊆ Aut C23164C2^3.6D464,136
C23.7D4 = C23.7D4φ: D4/C1D4 ⊆ Aut C23164C2^3.7D464,139
C23.8D4 = C4.9C42φ: D4/C2C22 ⊆ Aut C23164C2^3.8D464,18
C23.9D4 = C23.9D4φ: D4/C2C22 ⊆ Aut C2316C2^3.9D464,23
C23.10D4 = C23.10D4φ: D4/C2C22 ⊆ Aut C2332C2^3.10D464,75
C23.11D4 = C23.11D4φ: D4/C2C22 ⊆ Aut C2332C2^3.11D464,78
C23.12D4 = C2×C23⋊C4φ: D4/C2C22 ⊆ Aut C2316C2^3.12D464,90
C23.13D4 = C42⋊C22φ: D4/C2C22 ⊆ Aut C23164C2^3.13D464,102
C23.14D4 = D4⋊D4φ: D4/C2C22 ⊆ Aut C2332C2^3.14D464,130
C23.15D4 = D4.7D4φ: D4/C2C22 ⊆ Aut C2332C2^3.15D464,133
C23.16D4 = C8⋊D4φ: D4/C2C22 ⊆ Aut C2332C2^3.16D464,149
C23.17D4 = C82D4φ: D4/C2C22 ⊆ Aut C2332C2^3.17D464,150
C23.18D4 = C8.D4φ: D4/C2C22 ⊆ Aut C2332C2^3.18D464,151
C23.19D4 = C23.19D4φ: D4/C2C22 ⊆ Aut C2332C2^3.19D464,163
C23.20D4 = C23.20D4φ: D4/C2C22 ⊆ Aut C2332C2^3.20D464,166
C23.21D4 = D8⋊C22φ: D4/C2C22 ⊆ Aut C23164C2^3.21D464,256
C23.22D4 = C23.7Q8φ: D4/C4C2 ⊆ Aut C2332C2^3.22D464,61
C23.23D4 = C23.23D4φ: D4/C4C2 ⊆ Aut C2332C2^3.23D464,67
C23.24D4 = C23.24D4φ: D4/C4C2 ⊆ Aut C2332C2^3.24D464,97
C23.25D4 = C23.25D4φ: D4/C4C2 ⊆ Aut C2332C2^3.25D464,108
C23.26D4 = C88D4φ: D4/C4C2 ⊆ Aut C2332C2^3.26D464,146
C23.27D4 = C87D4φ: D4/C4C2 ⊆ Aut C2332C2^3.27D464,147
C23.28D4 = C8.18D4φ: D4/C4C2 ⊆ Aut C2332C2^3.28D464,148
C23.29D4 = C2×C4○D8φ: D4/C4C2 ⊆ Aut C2332C2^3.29D464,253
C23.30D4 = C22.SD16φ: D4/C22C2 ⊆ Aut C2316C2^3.30D464,8
C23.31D4 = C23.31D4φ: D4/C22C2 ⊆ Aut C2316C2^3.31D464,9
C23.32D4 = C426C4φ: D4/C22C2 ⊆ Aut C2316C2^3.32D464,20
C23.33D4 = C243C4φ: D4/C22C2 ⊆ Aut C2316C2^3.33D464,60
C23.34D4 = C23.34D4φ: D4/C22C2 ⊆ Aut C2332C2^3.34D464,62
C23.35D4 = C23.8Q8φ: D4/C22C2 ⊆ Aut C2332C2^3.35D464,66
C23.36D4 = C23.36D4φ: D4/C22C2 ⊆ Aut C2332C2^3.36D464,98
C23.37D4 = C23.37D4φ: D4/C22C2 ⊆ Aut C2316C2^3.37D464,99
C23.38D4 = C23.38D4φ: D4/C22C2 ⊆ Aut C2332C2^3.38D464,100
C23.39D4 = C2×C4≀C2φ: D4/C22C2 ⊆ Aut C2316C2^3.39D464,101
C23.40D4 = M4(2)⋊C4φ: D4/C22C2 ⊆ Aut C2332C2^3.40D464,109
C23.41D4 = C22⋊D8φ: D4/C22C2 ⊆ Aut C2316C2^3.41D464,128
C23.42D4 = Q8⋊D4φ: D4/C22C2 ⊆ Aut C2332C2^3.42D464,129
C23.43D4 = C22⋊SD16φ: D4/C22C2 ⊆ Aut C2316C2^3.43D464,131
C23.44D4 = C22⋊Q16φ: D4/C22C2 ⊆ Aut C2332C2^3.44D464,132
C23.45D4 = C22.D8φ: D4/C22C2 ⊆ Aut C2332C2^3.45D464,161
C23.46D4 = C23.46D4φ: D4/C22C2 ⊆ Aut C2332C2^3.46D464,162
C23.47D4 = C23.47D4φ: D4/C22C2 ⊆ Aut C2332C2^3.47D464,164
C23.48D4 = C23.48D4φ: D4/C22C2 ⊆ Aut C2332C2^3.48D464,165
C23.49D4 = C2×C22.D4φ: D4/C22C2 ⊆ Aut C2332C2^3.49D464,205
C23.50D4 = C2×C8⋊C22φ: D4/C22C2 ⊆ Aut C2316C2^3.50D464,254
C23.51D4 = C2×C8.C22φ: D4/C22C2 ⊆ Aut C2332C2^3.51D464,255
C23.52D4 = C22.4Q16central extension (φ=1)64C2^3.52D464,21
C23.53D4 = C2×C2.C42central extension (φ=1)64C2^3.53D464,56
C23.54D4 = C2×D4⋊C4central extension (φ=1)32C2^3.54D464,95
C23.55D4 = C2×Q8⋊C4central extension (φ=1)64C2^3.55D464,96
C23.56D4 = C2×C4.Q8central extension (φ=1)64C2^3.56D464,106
C23.57D4 = C2×C2.D8central extension (φ=1)64C2^3.57D464,107
C23.58D4 = C22×C22⋊C4central extension (φ=1)32C2^3.58D464,193
C23.59D4 = C22×C4⋊C4central extension (φ=1)64C2^3.59D464,194
C23.60D4 = C22×D8central extension (φ=1)32C2^3.60D464,250
C23.61D4 = C22×SD16central extension (φ=1)32C2^3.61D464,251
C23.62D4 = C22×Q16central extension (φ=1)64C2^3.62D464,252

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