# Extensions 1→N→G→Q→1 with N=C2×C3⋊S3 and Q=C22

Direct product G=N×Q with N=C2×C3⋊S3 and Q=C22
dρLabelID
C23×C3⋊S372C2^3xC3:S3144,196

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1C22 = S3×D12φ: C22/C1C22 ⊆ Out C2×C3⋊S3244+(C2xC3:S3):1C2^2144,144
(C2×C3⋊S3)⋊2C22 = S3×C3⋊D4φ: C22/C1C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3):2C2^2144,153
(C2×C3⋊S3)⋊3C22 = C2×C3⋊D12φ: C22/C2C2 ⊆ Out C2×C3⋊S324(C2xC3:S3):3C2^2144,151
(C2×C3⋊S3)⋊4C22 = Dic3⋊D6φ: C22/C2C2 ⊆ Out C2×C3⋊S3124+(C2xC3:S3):4C2^2144,154
(C2×C3⋊S3)⋊5C22 = C2×C12⋊S3φ: C22/C2C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):5C2^2144,170
(C2×C3⋊S3)⋊6C22 = D4×C3⋊S3φ: C22/C2C2 ⊆ Out C2×C3⋊S336(C2xC3:S3):6C2^2144,172
(C2×C3⋊S3)⋊7C22 = C2×C327D4φ: C22/C2C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):7C2^2144,177
(C2×C3⋊S3)⋊8C22 = C22×S32φ: C22/C2C2 ⊆ Out C2×C3⋊S324(C2xC3:S3):8C2^2144,192

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).1C22 = S32⋊C4φ: C22/C1C22 ⊆ Out C2×C3⋊S3124+(C2xC3:S3).1C2^2144,115
(C2×C3⋊S3).2C22 = C3⋊S3.Q8φ: C22/C1C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).2C2^2144,116
(C2×C3⋊S3).3C22 = C2.PSU3(𝔽2)φ: C22/C1C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).3C2^2144,120
(C2×C3⋊S3).4C22 = D6.6D6φ: C22/C1C22 ⊆ Out C2×C3⋊S3244+(C2xC3:S3).4C2^2144,142
(C2×C3⋊S3).5C22 = D6.3D6φ: C22/C1C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).5C2^2144,147
(C2×C3⋊S3).6C22 = C2×S3≀C2φ: C22/C1C22 ⊆ Out C2×C3⋊S3124+(C2xC3:S3).6C2^2144,186
(C2×C3⋊S3).7C22 = C2×PSU3(𝔽2)φ: C22/C1C22 ⊆ Out C2×C3⋊S3188+(C2xC3:S3).7C2^2144,187
(C2×C3⋊S3).8C22 = C4×C32⋊C4φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).8C2^2144,132
(C2×C3⋊S3).9C22 = C4⋊(C32⋊C4)φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).9C2^2144,133
(C2×C3⋊S3).10C22 = C62⋊C4φ: C22/C2C2 ⊆ Out C2×C3⋊S3124+(C2xC3:S3).10C2^2144,136
(C2×C3⋊S3).11C22 = D12⋊S3φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).11C2^2144,139
(C2×C3⋊S3).12C22 = Dic3.D6φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).12C2^2144,140
(C2×C3⋊S3).13C22 = D6.D6φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).13C2^2144,141
(C2×C3⋊S3).14C22 = C4×S32φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).14C2^2144,143
(C2×C3⋊S3).15C22 = D6⋊D6φ: C22/C2C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).15C2^2144,145
(C2×C3⋊S3).16C22 = C2×C6.D6φ: C22/C2C2 ⊆ Out C2×C3⋊S324(C2xC3:S3).16C2^2144,149
(C2×C3⋊S3).17C22 = C12.59D6φ: C22/C2C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).17C2^2144,171
(C2×C3⋊S3).18C22 = C12.D6φ: C22/C2C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).18C2^2144,173
(C2×C3⋊S3).19C22 = C12.26D6φ: C22/C2C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).19C2^2144,175
(C2×C3⋊S3).20C22 = C22×C32⋊C4φ: C22/C2C2 ⊆ Out C2×C3⋊S324(C2xC3:S3).20C2^2144,191
(C2×C3⋊S3).21C22 = C2×C4×C3⋊S3φ: trivial image72(C2xC3:S3).21C2^2144,169
(C2×C3⋊S3).22C22 = Q8×C3⋊S3φ: trivial image72(C2xC3:S3).22C2^2144,174

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