# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C23

Direct product G=N×Q with N=C3×C6 and Q=C23
dρLabelID
C22×C62144C2^2xC6^2144,197

Semidirect products G=N:Q with N=C3×C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊C23 = C22×S32φ: C23/C2C22 ⊆ Aut C3×C624(C3xC6):C2^3144,192
(C3×C6)⋊2C23 = S3×C22×C6φ: C23/C22C2 ⊆ Aut C3×C648(C3xC6):2C2^3144,195
(C3×C6)⋊3C23 = C23×C3⋊S3φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6):3C2^3144,196

Non-split extensions G=N.Q with N=C3×C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C3×C6).1C23 = S3×Dic6φ: C23/C2C22 ⊆ Aut C3×C6484-(C3xC6).1C2^3144,137
(C3×C6).2C23 = D125S3φ: C23/C2C22 ⊆ Aut C3×C6484-(C3xC6).2C2^3144,138
(C3×C6).3C23 = D12⋊S3φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).3C2^3144,139
(C3×C6).4C23 = Dic3.D6φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).4C2^3144,140
(C3×C6).5C23 = D6.D6φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).5C2^3144,141
(C3×C6).6C23 = D6.6D6φ: C23/C2C22 ⊆ Aut C3×C6244+(C3xC6).6C2^3144,142
(C3×C6).7C23 = C4×S32φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).7C2^3144,143
(C3×C6).8C23 = S3×D12φ: C23/C2C22 ⊆ Aut C3×C6244+(C3xC6).8C2^3144,144
(C3×C6).9C23 = D6⋊D6φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).9C2^3144,145
(C3×C6).10C23 = C2×S3×Dic3φ: C23/C2C22 ⊆ Aut C3×C648(C3xC6).10C2^3144,146
(C3×C6).11C23 = D6.3D6φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).11C2^3144,147
(C3×C6).12C23 = D6.4D6φ: C23/C2C22 ⊆ Aut C3×C6244-(C3xC6).12C2^3144,148
(C3×C6).13C23 = C2×C6.D6φ: C23/C2C22 ⊆ Aut C3×C624(C3xC6).13C2^3144,149
(C3×C6).14C23 = C2×D6⋊S3φ: C23/C2C22 ⊆ Aut C3×C648(C3xC6).14C2^3144,150
(C3×C6).15C23 = C2×C3⋊D12φ: C23/C2C22 ⊆ Aut C3×C624(C3xC6).15C2^3144,151
(C3×C6).16C23 = C2×C322Q8φ: C23/C2C22 ⊆ Aut C3×C648(C3xC6).16C2^3144,152
(C3×C6).17C23 = S3×C3⋊D4φ: C23/C2C22 ⊆ Aut C3×C6244(C3xC6).17C2^3144,153
(C3×C6).18C23 = Dic3⋊D6φ: C23/C2C22 ⊆ Aut C3×C6124+(C3xC6).18C2^3144,154
(C3×C6).19C23 = C6×Dic6φ: C23/C22C2 ⊆ Aut C3×C648(C3xC6).19C2^3144,158
(C3×C6).20C23 = S3×C2×C12φ: C23/C22C2 ⊆ Aut C3×C648(C3xC6).20C2^3144,159
(C3×C6).21C23 = C6×D12φ: C23/C22C2 ⊆ Aut C3×C648(C3xC6).21C2^3144,160
(C3×C6).22C23 = C3×C4○D12φ: C23/C22C2 ⊆ Aut C3×C6242(C3xC6).22C2^3144,161
(C3×C6).23C23 = C3×S3×D4φ: C23/C22C2 ⊆ Aut C3×C6244(C3xC6).23C2^3144,162
(C3×C6).24C23 = C3×D42S3φ: C23/C22C2 ⊆ Aut C3×C6244(C3xC6).24C2^3144,163
(C3×C6).25C23 = C3×S3×Q8φ: C23/C22C2 ⊆ Aut C3×C6484(C3xC6).25C2^3144,164
(C3×C6).26C23 = C3×Q83S3φ: C23/C22C2 ⊆ Aut C3×C6484(C3xC6).26C2^3144,165
(C3×C6).27C23 = Dic3×C2×C6φ: C23/C22C2 ⊆ Aut C3×C648(C3xC6).27C2^3144,166
(C3×C6).28C23 = C6×C3⋊D4φ: C23/C22C2 ⊆ Aut C3×C624(C3xC6).28C2^3144,167
(C3×C6).29C23 = C2×C324Q8φ: C23/C22C2 ⊆ Aut C3×C6144(C3xC6).29C2^3144,168
(C3×C6).30C23 = C2×C4×C3⋊S3φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).30C2^3144,169
(C3×C6).31C23 = C2×C12⋊S3φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).31C2^3144,170
(C3×C6).32C23 = C12.59D6φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).32C2^3144,171
(C3×C6).33C23 = D4×C3⋊S3φ: C23/C22C2 ⊆ Aut C3×C636(C3xC6).33C2^3144,172
(C3×C6).34C23 = C12.D6φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).34C2^3144,173
(C3×C6).35C23 = Q8×C3⋊S3φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).35C2^3144,174
(C3×C6).36C23 = C12.26D6φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).36C2^3144,175
(C3×C6).37C23 = C22×C3⋊Dic3φ: C23/C22C2 ⊆ Aut C3×C6144(C3xC6).37C2^3144,176
(C3×C6).38C23 = C2×C327D4φ: C23/C22C2 ⊆ Aut C3×C672(C3xC6).38C2^3144,177
(C3×C6).39C23 = D4×C3×C6central extension (φ=1)72(C3xC6).39C2^3144,179
(C3×C6).40C23 = Q8×C3×C6central extension (φ=1)144(C3xC6).40C2^3144,180
(C3×C6).41C23 = C32×C4○D4central extension (φ=1)72(C3xC6).41C2^3144,181

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