# Extensions 1→N→G→Q→1 with N=D4 and Q=C22×D7

Direct product G=N×Q with N=D4 and Q=C22×D7
dρLabelID
C22×D4×D7112C2^2xD4xD7448,1369

Semidirect products G=N:Q with N=D4 and Q=C22×D7
extensionφ:Q→Out NdρLabelID
D41(C22×D7) = C2×D7×D8φ: C22×D7/D14C2 ⊆ Out D4112D4:1(C2^2xD7)448,1207
D42(C22×D7) = C2×D8⋊D7φ: C22×D7/D14C2 ⊆ Out D4112D4:2(C2^2xD7)448,1208
D43(C22×D7) = D7×C8⋊C22φ: C22×D7/D14C2 ⊆ Out D4568+D4:3(C2^2xD7)448,1225
D44(C22×D7) = C22×D4⋊D7φ: C22×D7/C2×C14C2 ⊆ Out D4224D4:4(C2^2xD7)448,1245
D45(C22×D7) = C2×D4⋊D14φ: C22×D7/C2×C14C2 ⊆ Out D4112D4:5(C2^2xD7)448,1273
D46(C22×D7) = C22×D42D7φ: trivial image224D4:6(C2^2xD7)448,1370
D47(C22×D7) = C2×D46D14φ: trivial image112D4:7(C2^2xD7)448,1371
D48(C22×D7) = C2×D7×C4○D4φ: trivial image112D4:8(C2^2xD7)448,1375
D49(C22×D7) = C2×D48D14φ: trivial image112D4:9(C2^2xD7)448,1376
D410(C22×D7) = D7×2+ 1+4φ: trivial image568+D4:10(C2^2xD7)448,1379

Non-split extensions G=N.Q with N=D4 and Q=C22×D7
extensionφ:Q→Out NdρLabelID
D4.1(C22×D7) = C2×D83D7φ: C22×D7/D14C2 ⊆ Out D4224D4.1(C2^2xD7)448,1209
D4.2(C22×D7) = D813D14φ: C22×D7/D14C2 ⊆ Out D41124D4.2(C2^2xD7)448,1210
D4.3(C22×D7) = C2×D7×SD16φ: C22×D7/D14C2 ⊆ Out D4112D4.3(C2^2xD7)448,1211
D4.4(C22×D7) = C2×D56⋊C2φ: C22×D7/D14C2 ⊆ Out D4112D4.4(C2^2xD7)448,1212
D4.5(C22×D7) = C2×SD16⋊D7φ: C22×D7/D14C2 ⊆ Out D4224D4.5(C2^2xD7)448,1213
D4.6(C22×D7) = C2×SD163D7φ: C22×D7/D14C2 ⊆ Out D4224D4.6(C2^2xD7)448,1214
D4.7(C22×D7) = D28.29D4φ: C22×D7/D14C2 ⊆ Out D41124D4.7(C2^2xD7)448,1215
D4.8(C22×D7) = D7×C4○D8φ: C22×D7/D14C2 ⊆ Out D41124D4.8(C2^2xD7)448,1220
D4.9(C22×D7) = D810D14φ: C22×D7/D14C2 ⊆ Out D41124D4.9(C2^2xD7)448,1221
D4.10(C22×D7) = D815D14φ: C22×D7/D14C2 ⊆ Out D41124+D4.10(C2^2xD7)448,1222
D4.11(C22×D7) = D811D14φ: C22×D7/D14C2 ⊆ Out D41124D4.11(C2^2xD7)448,1223
D4.12(C22×D7) = D8.10D14φ: C22×D7/D14C2 ⊆ Out D42244-D4.12(C2^2xD7)448,1224
D4.13(C22×D7) = SD16⋊D14φ: C22×D7/D14C2 ⊆ Out D41128-D4.13(C2^2xD7)448,1226
D4.14(C22×D7) = D85D14φ: C22×D7/D14C2 ⊆ Out D41128+D4.14(C2^2xD7)448,1227
D4.15(C22×D7) = D86D14φ: C22×D7/D14C2 ⊆ Out D41128-D4.15(C2^2xD7)448,1228
D4.16(C22×D7) = D7×C8.C22φ: C22×D7/D14C2 ⊆ Out D41128-D4.16(C2^2xD7)448,1229
D4.17(C22×D7) = D56⋊C22φ: C22×D7/D14C2 ⊆ Out D41128+D4.17(C2^2xD7)448,1230
D4.18(C22×D7) = C56.C23φ: C22×D7/D14C2 ⊆ Out D41128+D4.18(C2^2xD7)448,1231
D4.19(C22×D7) = D28.44D4φ: C22×D7/D14C2 ⊆ Out D42248-D4.19(C2^2xD7)448,1232
D4.20(C22×D7) = C2×D4.D14φ: C22×D7/C2×C14C2 ⊆ Out D4112D4.20(C2^2xD7)448,1246
D4.21(C22×D7) = C22×D4.D7φ: C22×D7/C2×C14C2 ⊆ Out D4224D4.21(C2^2xD7)448,1247
D4.22(C22×D7) = C2×D4.8D14φ: C22×D7/C2×C14C2 ⊆ Out D4224D4.22(C2^2xD7)448,1274
D4.23(C22×D7) = C28.C24φ: C22×D7/C2×C14C2 ⊆ Out D41124D4.23(C2^2xD7)448,1275
D4.24(C22×D7) = C2×D4.9D14φ: C22×D7/C2×C14C2 ⊆ Out D4224D4.24(C2^2xD7)448,1276
D4.25(C22×D7) = D28.32C23φ: C22×D7/C2×C14C2 ⊆ Out D41128+D4.25(C2^2xD7)448,1288
D4.26(C22×D7) = D28.33C23φ: C22×D7/C2×C14C2 ⊆ Out D41128-D4.26(C2^2xD7)448,1289
D4.27(C22×D7) = D28.34C23φ: C22×D7/C2×C14C2 ⊆ Out D41128+D4.27(C2^2xD7)448,1290
D4.28(C22×D7) = D28.35C23φ: C22×D7/C2×C14C2 ⊆ Out D42248-D4.28(C2^2xD7)448,1291
D4.29(C22×D7) = C2×D4.10D14φ: trivial image224D4.29(C2^2xD7)448,1377
D4.30(C22×D7) = C14.C25φ: trivial image1124D4.30(C2^2xD7)448,1378
D4.31(C22×D7) = D14.C24φ: trivial image1128-D4.31(C2^2xD7)448,1380
D4.32(C22×D7) = D7×2- 1+4φ: trivial image1128-D4.32(C2^2xD7)448,1381
D4.33(C22×D7) = D28.39C23φ: trivial image1128+D4.33(C2^2xD7)448,1382

׿
×
𝔽