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

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

Semidirect products G=N:Q with N=S3×C20 and Q=C22
extensionφ:Q→Out NdρLabelID
(S3×C20)⋊1C22 = S3×D4×D5φ: C22/C1 → C22 ⊆ Out S3×C20608+(S3xC20):1C2^2480,1097
(S3×C20)⋊2C22 = D5×D4⋊2S3φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20):2C2^2480,1098
(S3×C20)⋊3C22 = D30.C23φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20):3C2^2480,1100
(S3×C20)⋊4C22 = D20⋊13D6φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20):4C2^2480,1101
(S3×C20)⋊5C22 = D20⋊14D6φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20):5C2^2480,1102
(S3×C20)⋊6C22 = D12⋊14D10φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20):6C2^2480,1103
(S3×C20)⋊7C22 = D5×Q8⋊3S3φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20):7C2^2480,1108
(S3×C20)⋊8C22 = D20⋊16D6φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20):8C2^2480,1110
(S3×C20)⋊9C22 = D20⋊17D6φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20):9C2^2480,1111
(S3×C20)⋊10C22 = D20⋊25D6φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20):10C2^2480,1093
(S3×C20)⋊11C22 = D20⋊29D6φ: C22/C1 → C22 ⊆ Out S3×C201204+(S3xC20):11C2^2480,1095
(S3×C20)⋊12C22 = D5×C4○D12φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20):12C2^2480,1090
(S3×C20)⋊13C22 = D20⋊24D6φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20):13C2^2480,1092
(S3×C20)⋊14C22 = C5×D4⋊6D6φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20):14C2^2480,1156
(S3×C20)⋊15C22 = C5×D4○D12φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20):15C2^2480,1161
(S3×C20)⋊16C22 = C2×D20⋊5S3φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):16C2^2480,1074
(S3×C20)⋊17C22 = C2×D60⋊C2φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):17C2^2480,1081
(S3×C20)⋊18C22 = C2×S3×D20φ: C22/C2 → C2 ⊆ Out S3×C20120(S3xC20):18C2^2480,1088
(S3×C20)⋊19C22 = C2×D6.D10φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):19C2^2480,1083
(S3×C20)⋊20C22 = S3×C2×C4×D5φ: C22/C2 → C2 ⊆ Out S3×C20120(S3xC20):20C2^2480,1086
(S3×C20)⋊21C22 = S3×C4○D20φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20):21C2^2480,1091
(S3×C20)⋊22C22 = S3×D4×C10φ: C22/C2 → C2 ⊆ Out S3×C20120(S3xC20):22C2^2480,1154
(S3×C20)⋊23C22 = C10×D4⋊2S3φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):23C2^2480,1155
(S3×C20)⋊24C22 = C10×Q8⋊3S3φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):24C2^2480,1158
(S3×C20)⋊25C22 = C10×C4○D12φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20):25C2^2480,1153
(S3×C20)⋊26C22 = C5×S3×C4○D4φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20):26C2^2480,1160

Non-split extensions G=N.Q with N=S3×C20 and Q=C22
extensionφ:Q→Out NdρLabelID
(S3×C20).1C22 = S3×D4⋊D5φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).1C2^2480,555
(S3×C20).2C22 = D60.C22φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).2C2^2480,556
(S3×C20).3C22 = S3×D4.D5φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20).3C2^2480,561
(S3×C20).4C22 = C60.10C23φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).4C2^2480,562
(S3×C20).5C22 = D20.24D6φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).5C2^2480,569
(S3×C20).6C22 = D20⋊10D6φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20).6C2^2480,570
(S3×C20).7C22 = C60.19C23φ: C22/C1 → C22 ⊆ Out S3×C202408+(S3xC20).7C2^2480,571
(S3×C20).8C22 = D12.9D10φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).8C2^2480,572
(S3×C20).9C22 = S3×Q8⋊D5φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).9C2^2480,579
(S3×C20).10C22 = D12⋊D10φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).10C2^2480,580
(S3×C20).11C22 = S3×C5⋊Q16φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).11C2^2480,585
(S3×C20).12C22 = Dic10.26D6φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).12C2^2480,586
(S3×C20).13C22 = D20.27D6φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).13C2^2480,593
(S3×C20).14C22 = D20.28D6φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).14C2^2480,594
(S3×C20).15C22 = Dic10.27D6φ: C22/C1 → C22 ⊆ Out S3×C202408+(S3xC20).15C2^2480,595
(S3×C20).16C22 = C60.44C23φ: C22/C1 → C22 ⊆ Out S3×C202408+(S3xC20).16C2^2480,596
(S3×C20).17C22 = C15⋊2- 1+4φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).17C2^2480,1096
(S3×C20).18C22 = S3×D4⋊2D5φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20).18C2^2480,1099
(S3×C20).19C22 = D20.29D6φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).19C2^2480,1104
(S3×C20).20C22 = C30.33C24φ: C22/C1 → C22 ⊆ Out S3×C202408+(S3xC20).20C2^2480,1105
(S3×C20).21C22 = D12.29D10φ: C22/C1 → C22 ⊆ Out S3×C202408-(S3xC20).21C2^2480,1106
(S3×C20).22C22 = S3×Q8×D5φ: C22/C1 → C22 ⊆ Out S3×C201208-(S3xC20).22C2^2480,1107
(S3×C20).23C22 = S3×Q8⋊2D5φ: C22/C1 → C22 ⊆ Out S3×C201208+(S3xC20).23C2^2480,1109
(S3×C20).24C22 = C40⋊1D6φ: C22/C1 → C22 ⊆ Out S3×C201204+(S3xC20).24C2^2480,329
(S3×C20).25C22 = D40⋊S3φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20).25C2^2480,330
(S3×C20).26C22 = Dic20⋊S3φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).26C2^2480,339
(S3×C20).27C22 = C40.2D6φ: C22/C1 → C22 ⊆ Out S3×C202404-(S3xC20).27C2^2480,350
(S3×C20).28C22 = D20.39D6φ: C22/C1 → C22 ⊆ Out S3×C202404-(S3xC20).28C2^2480,1077
(S3×C20).29C22 = C30.C24φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).29C2^2480,1080
(S3×C20).30C22 = D5×C8⋊S3φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20).30C2^2480,320
(S3×C20).31C22 = C40⋊D6φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20).31C2^2480,322
(S3×C20).32C22 = C40.34D6φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).32C2^2480,342
(S3×C20).33C22 = C40.35D6φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).33C2^2480,344
(S3×C20).34C22 = D12.2Dic5φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).34C2^2480,362
(S3×C20).35C22 = D12.Dic5φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).35C2^2480,364
(S3×C20).36C22 = C5×D8⋊S3φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20).36C2^2480,790
(S3×C20).37C22 = C5×Q8⋊3D6φ: C22/C1 → C22 ⊆ Out S3×C201204(S3xC20).37C2^2480,793
(S3×C20).38C22 = C5×D4.D6φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).38C2^2480,794
(S3×C20).39C22 = C5×Q16⋊S3φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).39C2^2480,797
(S3×C20).40C22 = C5×Q8.15D6φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).40C2^2480,1159
(S3×C20).41C22 = C5×Q8○D12φ: C22/C1 → C22 ⊆ Out S3×C202404(S3xC20).41C2^2480,1162
(S3×C20).42C22 = S3×C40⋊C2φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).42C2^2480,327
(S3×C20).43C22 = S3×D40φ: C22/C2 → C2 ⊆ Out S3×C201204+(S3xC20).43C2^2480,328
(S3×C20).44C22 = S3×Dic20φ: C22/C2 → C2 ⊆ Out S3×C202404-(S3xC20).44C2^2480,338
(S3×C20).45C22 = D6.1D20φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).45C2^2480,348
(S3×C20).46C22 = D40⋊7S3φ: C22/C2 → C2 ⊆ Out S3×C202404-(S3xC20).46C2^2480,349
(S3×C20).47C22 = D120⋊5C2φ: C22/C2 → C2 ⊆ Out S3×C202404+(S3xC20).47C2^2480,351
(S3×C20).48C22 = C2×S3×Dic10φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20).48C2^2480,1078
(S3×C20).49C22 = S3×C8×D5φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).49C2^2480,319
(S3×C20).50C22 = S3×C8⋊D5φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).50C2^2480,321
(S3×C20).51C22 = C40.54D6φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).51C2^2480,341
(S3×C20).52C22 = C40.55D6φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).52C2^2480,343
(S3×C20).53C22 = C2×S3×C5⋊2C8φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20).53C2^2480,361
(S3×C20).54C22 = S3×C4.Dic5φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).54C2^2480,363
(S3×C20).55C22 = C2×D6.Dic5φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20).55C2^2480,370
(S3×C20).56C22 = C5×S3×D8φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).56C2^2480,789
(S3×C20).57C22 = C5×D8⋊3S3φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).57C2^2480,791
(S3×C20).58C22 = C5×S3×SD16φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).58C2^2480,792
(S3×C20).59C22 = C5×Q8.7D6φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).59C2^2480,795
(S3×C20).60C22 = C5×S3×Q16φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).60C2^2480,796
(S3×C20).61C22 = C5×D24⋊C2φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).61C2^2480,798
(S3×C20).62C22 = S3×Q8×C10φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20).62C2^2480,1157
(S3×C20).63C22 = C10×C8⋊S3φ: C22/C2 → C2 ⊆ Out S3×C20240(S3xC20).63C2^2480,779
(S3×C20).64C22 = C5×C8○D12φ: C22/C2 → C2 ⊆ Out S3×C202402(S3xC20).64C2^2480,780
(S3×C20).65C22 = C5×S3×M4(2)φ: C22/C2 → C2 ⊆ Out S3×C201204(S3xC20).65C2^2480,785
(S3×C20).66C22 = C5×D12.C4φ: C22/C2 → C2 ⊆ Out S3×C202404(S3xC20).66C2^2480,786
(S3×C20).67C22 = S3×C2×C40φ: trivial image240(S3xC20).67C2^2480,778

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