# Extensions 1→N→G→Q→1 with N=C22×C4 and Q=S3

Direct product G=N×Q with N=C22×C4 and Q=S3
dρLabelID
S3×C22×C448S3xC2^2xC496,206

Semidirect products G=N:Q with N=C22×C4 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C4)⋊1S3 = C4×S4φ: S3/C1S3 ⊆ Aut C22×C4123(C2^2xC4):1S396,186
(C22×C4)⋊2S3 = C4⋊S4φ: S3/C1S3 ⊆ Aut C22×C4126+(C2^2xC4):2S396,187
(C22×C4)⋊3S3 = C2×D6⋊C4φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):3S396,134
(C22×C4)⋊4S3 = C4×C3⋊D4φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):4S396,135
(C22×C4)⋊5S3 = C23.28D6φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):5S396,136
(C22×C4)⋊6S3 = C127D4φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):6S396,137
(C22×C4)⋊7S3 = C22×D12φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):7S396,207
(C22×C4)⋊8S3 = C2×C4○D12φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4):8S396,208

Non-split extensions G=N.Q with N=C22×C4 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C4).1S3 = A4⋊C8φ: S3/C1S3 ⊆ Aut C22×C4243(C2^2xC4).1S396,65
(C22×C4).2S3 = A4⋊Q8φ: S3/C1S3 ⊆ Aut C22×C4246-(C2^2xC4).2S396,185
(C22×C4).3S3 = C12.55D4φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4).3S396,37
(C22×C4).4S3 = C6.C42φ: S3/C3C2 ⊆ Aut C22×C496(C2^2xC4).4S396,38
(C22×C4).5S3 = C2×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C22×C496(C2^2xC4).5S396,130
(C22×C4).6S3 = C2×C4.Dic3φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4).6S396,128
(C22×C4).7S3 = C12.48D4φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4).7S396,131
(C22×C4).8S3 = C2×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C496(C2^2xC4).8S396,132
(C22×C4).9S3 = C23.26D6φ: S3/C3C2 ⊆ Aut C22×C448(C2^2xC4).9S396,133
(C22×C4).10S3 = C22×Dic6φ: S3/C3C2 ⊆ Aut C22×C496(C2^2xC4).10S396,205
(C22×C4).11S3 = C22×C3⋊C8central extension (φ=1)96(C2^2xC4).11S396,127
(C22×C4).12S3 = C2×C4×Dic3central extension (φ=1)96(C2^2xC4).12S396,129

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