# Extensions 1→N→G→Q→1 with N=C23 and Q=D6

Direct product G=N×Q with N=C23 and Q=D6
dρLabelID
S3×C2448S3xC2^496,230

Semidirect products G=N:Q with N=C23 and Q=D6
extensionφ:Q→Aut NdρLabelID
C23⋊D6 = C22×S4φ: D6/C2S3 ⊆ Aut C2312C2^3:D696,226
C232D6 = C232D6φ: D6/C3C22 ⊆ Aut C2324C2^3:2D696,144
C233D6 = D46D6φ: D6/C3C22 ⊆ Aut C23244C2^3:3D696,211
C234D6 = C2×S3×D4φ: D6/S3C2 ⊆ Aut C2324C2^3:4D696,209
C235D6 = C22×C3⋊D4φ: D6/C6C2 ⊆ Aut C2348C2^3:5D696,219

Non-split extensions G=N.Q with N=C23 and Q=D6
extensionφ:Q→Aut NdρLabelID
C23.1D6 = A4⋊Q8φ: D6/C2S3 ⊆ Aut C23246-C2^3.1D696,185
C23.2D6 = C4×S4φ: D6/C2S3 ⊆ Aut C23123C2^3.2D696,186
C23.3D6 = C4⋊S4φ: D6/C2S3 ⊆ Aut C23126+C2^3.3D696,187
C23.4D6 = C2×A4⋊C4φ: D6/C2S3 ⊆ Aut C2324C2^3.4D696,194
C23.5D6 = A4⋊D4φ: D6/C2S3 ⊆ Aut C23126+C2^3.5D696,195
C23.6D6 = C23.6D6φ: D6/C3C22 ⊆ Aut C23244C2^3.6D696,13
C23.7D6 = C23.7D6φ: D6/C3C22 ⊆ Aut C23244C2^3.7D696,41
C23.8D6 = C23.8D6φ: D6/C3C22 ⊆ Aut C2348C2^3.8D696,86
C23.9D6 = C23.9D6φ: D6/C3C22 ⊆ Aut C2348C2^3.9D696,90
C23.10D6 = Dic3⋊D4φ: D6/C3C22 ⊆ Aut C2348C2^3.10D696,91
C23.11D6 = C23.11D6φ: D6/C3C22 ⊆ Aut C2348C2^3.11D696,92
C23.12D6 = C23.12D6φ: D6/C3C22 ⊆ Aut C2348C2^3.12D696,143
C23.13D6 = D63D4φ: D6/C3C22 ⊆ Aut C2348C2^3.13D696,145
C23.14D6 = C23.14D6φ: D6/C3C22 ⊆ Aut C2348C2^3.14D696,146
C23.15D6 = C123D4φ: D6/C3C22 ⊆ Aut C2348C2^3.15D696,147
C23.16D6 = C23.16D6φ: D6/S3C2 ⊆ Aut C2348C2^3.16D696,84
C23.17D6 = Dic3.D4φ: D6/S3C2 ⊆ Aut C2348C2^3.17D696,85
C23.18D6 = S3×C22⋊C4φ: D6/S3C2 ⊆ Aut C2324C2^3.18D696,87
C23.19D6 = Dic34D4φ: D6/S3C2 ⊆ Aut C2348C2^3.19D696,88
C23.20D6 = D6⋊D4φ: D6/S3C2 ⊆ Aut C2324C2^3.20D696,89
C23.21D6 = C23.21D6φ: D6/S3C2 ⊆ Aut C2348C2^3.21D696,93
C23.22D6 = D4×Dic3φ: D6/S3C2 ⊆ Aut C2348C2^3.22D696,141
C23.23D6 = C23.23D6φ: D6/S3C2 ⊆ Aut C2348C2^3.23D696,142
C23.24D6 = C2×D42S3φ: D6/S3C2 ⊆ Aut C2348C2^3.24D696,210
C23.25D6 = C12.48D4φ: D6/C6C2 ⊆ Aut C2348C2^3.25D696,131
C23.26D6 = C23.26D6φ: D6/C6C2 ⊆ Aut C2348C2^3.26D696,133
C23.27D6 = C4×C3⋊D4φ: D6/C6C2 ⊆ Aut C2348C2^3.27D696,135
C23.28D6 = C23.28D6φ: D6/C6C2 ⊆ Aut C2348C2^3.28D696,136
C23.29D6 = C127D4φ: D6/C6C2 ⊆ Aut C2348C2^3.29D696,137
C23.30D6 = C244S3φ: D6/C6C2 ⊆ Aut C2324C2^3.30D696,160
C23.31D6 = C2×C4○D12φ: D6/C6C2 ⊆ Aut C2348C2^3.31D696,208
C23.32D6 = C6.C42central extension (φ=1)96C2^3.32D696,38
C23.33D6 = C2×C4×Dic3central extension (φ=1)96C2^3.33D696,129
C23.34D6 = C2×Dic3⋊C4central extension (φ=1)96C2^3.34D696,130
C23.35D6 = C2×C4⋊Dic3central extension (φ=1)96C2^3.35D696,132
C23.36D6 = C2×D6⋊C4central extension (φ=1)48C2^3.36D696,134
C23.37D6 = C2×C6.D4central extension (φ=1)48C2^3.37D696,159
C23.38D6 = C22×Dic6central extension (φ=1)96C2^3.38D696,205
C23.39D6 = S3×C22×C4central extension (φ=1)48C2^3.39D696,206
C23.40D6 = C22×D12central extension (φ=1)48C2^3.40D696,207
C23.41D6 = C23×Dic3central extension (φ=1)96C2^3.41D696,218

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