# Extensions 1→N→G→Q→1 with N=C22×C20 and Q=S3

Direct product G=N×Q with N=C22×C20 and Q=S3
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=C22×C20 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C20)⋊1S3 = C20×S4φ: S3/C1S3 ⊆ Aut C22×C20603(C2^2xC20):1S3480,1014
(C22×C20)⋊2S3 = C20⋊S4φ: S3/C1S3 ⊆ Aut C22×C20606+(C2^2xC20):2S3480,1026
(C22×C20)⋊3S3 = C4×C5⋊S4φ: S3/C1S3 ⊆ Aut C22×C20606(C2^2xC20):3S3480,1025
(C22×C20)⋊4S3 = C5×C4⋊S4φ: S3/C1S3 ⊆ Aut C22×C20606(C2^2xC20):4S3480,1015
(C22×C20)⋊5S3 = C10×D6⋊C4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):5S3480,806
(C22×C20)⋊6S3 = C20×C3⋊D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):6S3480,807
(C22×C20)⋊7S3 = C5×C23.28D6φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):7S3480,808
(C22×C20)⋊8S3 = C2×D303C4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):8S3480,892
(C22×C20)⋊9S3 = C23.28D30φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):9S3480,894
(C22×C20)⋊10S3 = C6029D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):10S3480,895
(C22×C20)⋊11S3 = C22×D60φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):11S3480,1167
(C22×C20)⋊12S3 = C2×D6011C2φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):12S3480,1168
(C22×C20)⋊13S3 = C4×C157D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):13S3480,893
(C22×C20)⋊14S3 = C22×C4×D15φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):14S3480,1166
(C22×C20)⋊15S3 = C5×C127D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):15S3480,809
(C22×C20)⋊16S3 = C2×C10×D12φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):16S3480,1152
(C22×C20)⋊17S3 = C10×C4○D12φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20):17S3480,1153

Non-split extensions G=N.Q with N=C22×C20 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C20).1S3 = C5×A4⋊C8φ: S3/C1S3 ⊆ Aut C22×C201203(C2^2xC20).1S3480,255
(C22×C20).2S3 = C20.1S4φ: S3/C1S3 ⊆ Aut C22×C201206-(C2^2xC20).2S3480,1024
(C22×C20).3S3 = C20.S4φ: S3/C1S3 ⊆ Aut C22×C201206(C2^2xC20).3S3480,259
(C22×C20).4S3 = C5×A4⋊Q8φ: S3/C1S3 ⊆ Aut C22×C201206(C2^2xC20).4S3480,1013
(C22×C20).5S3 = C5×C12.55D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).5S3480,149
(C22×C20).6S3 = C5×C6.C42φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).6S3480,150
(C22×C20).7S3 = C30.29C42φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).7S3480,191
(C22×C20).8S3 = C10×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).8S3480,802
(C22×C20).9S3 = C2×C30.4Q8φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).9S3480,888
(C22×C20).10S3 = C60.205D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).10S3480,889
(C22×C20).11S3 = C2×C605C4φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).11S3480,890
(C22×C20).12S3 = C22×Dic30φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).12S3480,1165
(C22×C20).13S3 = C2×C60.7C4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).13S3480,886
(C22×C20).14S3 = C23.26D30φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).14S3480,891
(C22×C20).15S3 = C60.212D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).15S3480,190
(C22×C20).16S3 = C22×C153C8φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).16S3480,885
(C22×C20).17S3 = C2×C4×Dic15φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).17S3480,887
(C22×C20).18S3 = C10×C4.Dic3φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).18S3480,800
(C22×C20).19S3 = C5×C12.48D4φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).19S3480,803
(C22×C20).20S3 = C10×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).20S3480,804
(C22×C20).21S3 = C5×C23.26D6φ: S3/C3C2 ⊆ Aut C22×C20240(C2^2xC20).21S3480,805
(C22×C20).22S3 = C2×C10×Dic6φ: S3/C3C2 ⊆ Aut C22×C20480(C2^2xC20).22S3480,1150
(C22×C20).23S3 = C2×C10×C3⋊C8central extension (φ=1)480(C2^2xC20).23S3480,799
(C22×C20).24S3 = Dic3×C2×C20central extension (φ=1)480(C2^2xC20).24S3480,801

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