# Extensions 1→N→G→Q→1 with N=C7×D4 and Q=C23

Direct product G=N×Q with N=C7×D4 and Q=C23
dρLabelID
D4×C22×C14224D4xC2^2xC14448,1386

Semidirect products G=N:Q with N=C7×D4 and Q=C23
extensionφ:Q→Out NdρLabelID
(C7×D4)⋊1C23 = C2×D7×D8φ: C23/C2C22 ⊆ Out C7×D4112(C7xD4):1C2^3448,1207
(C7×D4)⋊2C23 = C2×D8⋊D7φ: C23/C2C22 ⊆ Out C7×D4112(C7xD4):2C2^3448,1208
(C7×D4)⋊3C23 = D7×C8⋊C22φ: C23/C2C22 ⊆ Out C7×D4568+(C7xD4):3C2^3448,1225
(C7×D4)⋊4C23 = C22×D4⋊D7φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4):4C2^3448,1245
(C7×D4)⋊5C23 = C2×D4⋊D14φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):5C2^3448,1273
(C7×D4)⋊6C23 = C22×D4×D7φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):6C2^3448,1369
(C7×D4)⋊7C23 = C22×D42D7φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4):7C2^3448,1370
(C7×D4)⋊8C23 = C2×D46D14φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):8C2^3448,1371
(C7×D4)⋊9C23 = C2×D7×C4○D4φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):9C2^3448,1375
(C7×D4)⋊10C23 = C2×D48D14φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):10C2^3448,1376
(C7×D4)⋊11C23 = D7×2+ 1+4φ: C23/C22C2 ⊆ Out C7×D4568+(C7xD4):11C2^3448,1379
(C7×D4)⋊12C23 = D8×C2×C14φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4):12C2^3448,1352
(C7×D4)⋊13C23 = C14×C8⋊C22φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4):13C2^3448,1356
(C7×D4)⋊14C23 = C4○D4×C2×C14φ: trivial image224(C7xD4):14C2^3448,1388
(C7×D4)⋊15C23 = C14×2+ 1+4φ: trivial image112(C7xD4):15C2^3448,1389

Non-split extensions G=N.Q with N=C7×D4 and Q=C23
extensionφ:Q→Out NdρLabelID
(C7×D4).1C23 = C2×D83D7φ: C23/C2C22 ⊆ Out C7×D4224(C7xD4).1C2^3448,1209
(C7×D4).2C23 = D813D14φ: C23/C2C22 ⊆ Out C7×D41124(C7xD4).2C2^3448,1210
(C7×D4).3C23 = C2×D7×SD16φ: C23/C2C22 ⊆ Out C7×D4112(C7xD4).3C2^3448,1211
(C7×D4).4C23 = C2×D56⋊C2φ: C23/C2C22 ⊆ Out C7×D4112(C7xD4).4C2^3448,1212
(C7×D4).5C23 = C2×SD16⋊D7φ: C23/C2C22 ⊆ Out C7×D4224(C7xD4).5C2^3448,1213
(C7×D4).6C23 = C2×SD163D7φ: C23/C2C22 ⊆ Out C7×D4224(C7xD4).6C2^3448,1214
(C7×D4).7C23 = D28.29D4φ: C23/C2C22 ⊆ Out C7×D41124(C7xD4).7C2^3448,1215
(C7×D4).8C23 = D7×C4○D8φ: C23/C2C22 ⊆ Out C7×D41124(C7xD4).8C2^3448,1220
(C7×D4).9C23 = D810D14φ: C23/C2C22 ⊆ Out C7×D41124(C7xD4).9C2^3448,1221
(C7×D4).10C23 = D815D14φ: C23/C2C22 ⊆ Out C7×D41124+(C7xD4).10C2^3448,1222
(C7×D4).11C23 = D811D14φ: C23/C2C22 ⊆ Out C7×D41124(C7xD4).11C2^3448,1223
(C7×D4).12C23 = D8.10D14φ: C23/C2C22 ⊆ Out C7×D42244-(C7xD4).12C2^3448,1224
(C7×D4).13C23 = SD16⋊D14φ: C23/C2C22 ⊆ Out C7×D41128-(C7xD4).13C2^3448,1226
(C7×D4).14C23 = D85D14φ: C23/C2C22 ⊆ Out C7×D41128+(C7xD4).14C2^3448,1227
(C7×D4).15C23 = D86D14φ: C23/C2C22 ⊆ Out C7×D41128-(C7xD4).15C2^3448,1228
(C7×D4).16C23 = D7×C8.C22φ: C23/C2C22 ⊆ Out C7×D41128-(C7xD4).16C2^3448,1229
(C7×D4).17C23 = D56⋊C22φ: C23/C2C22 ⊆ Out C7×D41128+(C7xD4).17C2^3448,1230
(C7×D4).18C23 = C56.C23φ: C23/C2C22 ⊆ Out C7×D41128+(C7xD4).18C2^3448,1231
(C7×D4).19C23 = D28.44D4φ: C23/C2C22 ⊆ Out C7×D42248-(C7xD4).19C2^3448,1232
(C7×D4).20C23 = C2×D4.D14φ: C23/C22C2 ⊆ Out C7×D4112(C7xD4).20C2^3448,1246
(C7×D4).21C23 = C22×D4.D7φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).21C2^3448,1247
(C7×D4).22C23 = C2×D4.8D14φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).22C2^3448,1274
(C7×D4).23C23 = C28.C24φ: C23/C22C2 ⊆ Out C7×D41124(C7xD4).23C2^3448,1275
(C7×D4).24C23 = C2×D4.9D14φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).24C2^3448,1276
(C7×D4).25C23 = D28.32C23φ: C23/C22C2 ⊆ Out C7×D41128+(C7xD4).25C2^3448,1288
(C7×D4).26C23 = D28.33C23φ: C23/C22C2 ⊆ Out C7×D41128-(C7xD4).26C2^3448,1289
(C7×D4).27C23 = D28.34C23φ: C23/C22C2 ⊆ Out C7×D41128+(C7xD4).27C2^3448,1290
(C7×D4).28C23 = D28.35C23φ: C23/C22C2 ⊆ Out C7×D42248-(C7xD4).28C2^3448,1291
(C7×D4).29C23 = C2×D4.10D14φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).29C2^3448,1377
(C7×D4).30C23 = C14.C25φ: C23/C22C2 ⊆ Out C7×D41124(C7xD4).30C2^3448,1378
(C7×D4).31C23 = D14.C24φ: C23/C22C2 ⊆ Out C7×D41128-(C7xD4).31C2^3448,1380
(C7×D4).32C23 = D7×2- 1+4φ: C23/C22C2 ⊆ Out C7×D41128-(C7xD4).32C2^3448,1381
(C7×D4).33C23 = D28.39C23φ: C23/C22C2 ⊆ Out C7×D41128+(C7xD4).33C2^3448,1382
(C7×D4).34C23 = SD16×C2×C14φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).34C2^3448,1353
(C7×D4).35C23 = C14×C4○D8φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).35C2^3448,1355
(C7×D4).36C23 = C14×C8.C22φ: C23/C22C2 ⊆ Out C7×D4224(C7xD4).36C2^3448,1357
(C7×D4).37C23 = C7×D8⋊C22φ: C23/C22C2 ⊆ Out C7×D41124(C7xD4).37C2^3448,1358
(C7×D4).38C23 = C7×D4○D8φ: C23/C22C2 ⊆ Out C7×D41124(C7xD4).38C2^3448,1359
(C7×D4).39C23 = C7×D4○SD16φ: C23/C22C2 ⊆ Out C7×D41124(C7xD4).39C2^3448,1360
(C7×D4).40C23 = C7×Q8○D8φ: C23/C22C2 ⊆ Out C7×D42244(C7xD4).40C2^3448,1361
(C7×D4).41C23 = C14×2- 1+4φ: trivial image224(C7xD4).41C2^3448,1390
(C7×D4).42C23 = C7×C2.C25φ: trivial image1124(C7xD4).42C2^3448,1391

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