# Extensions 1→N→G→Q→1 with N=C8 and Q=C22×D7

Direct product G=N×Q with N=C8 and Q=C22×D7
dρLabelID
D7×C22×C8224D7xC2^2xC8448,1189

Semidirect products G=N:Q with N=C8 and Q=C22×D7
extensionφ:Q→Aut NdρLabelID
C81(C22×D7) = D7×C8⋊C22φ: C22×D7/D7C22 ⊆ Aut C8568+C8:1(C2^2xD7)448,1225
C82(C22×D7) = C2×C8⋊D14φ: C22×D7/C14C22 ⊆ Aut C8112C8:2(C2^2xD7)448,1199
C83(C22×D7) = C2×D8⋊D7φ: C22×D7/C14C22 ⊆ Aut C8112C8:3(C2^2xD7)448,1208
C84(C22×D7) = C2×D56⋊C2φ: C22×D7/C14C22 ⊆ Aut C8112C8:4(C2^2xD7)448,1212
C85(C22×D7) = C2×D7×D8φ: C22×D7/D14C2 ⊆ Aut C8112C8:5(C2^2xD7)448,1207
C86(C22×D7) = C2×D7×SD16φ: C22×D7/D14C2 ⊆ Aut C8112C8:6(C2^2xD7)448,1211
C87(C22×D7) = C2×D7×M4(2)φ: C22×D7/D14C2 ⊆ Aut C8112C8:7(C2^2xD7)448,1196
C88(C22×D7) = C22×D56φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8:8(C2^2xD7)448,1193
C89(C22×D7) = C22×C56⋊C2φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8:9(C2^2xD7)448,1192
C810(C22×D7) = C22×C8⋊D7φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8:10(C2^2xD7)448,1190

Non-split extensions G=N.Q with N=C8 and Q=C22×D7
extensionφ:Q→Aut NdρLabelID
C8.1(C22×D7) = SD16⋊D14φ: C22×D7/D7C22 ⊆ Aut C81128-C8.1(C2^2xD7)448,1226
C8.2(C22×D7) = D85D14φ: C22×D7/D7C22 ⊆ Aut C81128+C8.2(C2^2xD7)448,1227
C8.3(C22×D7) = D86D14φ: C22×D7/D7C22 ⊆ Aut C81128-C8.3(C2^2xD7)448,1228
C8.4(C22×D7) = D7×C8.C22φ: C22×D7/D7C22 ⊆ Aut C81128-C8.4(C2^2xD7)448,1229
C8.5(C22×D7) = D56⋊C22φ: C22×D7/D7C22 ⊆ Aut C81128+C8.5(C2^2xD7)448,1230
C8.6(C22×D7) = C56.C23φ: C22×D7/D7C22 ⊆ Aut C81128+C8.6(C2^2xD7)448,1231
C8.7(C22×D7) = D28.44D4φ: C22×D7/D7C22 ⊆ Aut C82248-C8.7(C2^2xD7)448,1232
C8.8(C22×D7) = C2×C8.D14φ: C22×D7/C14C22 ⊆ Aut C8224C8.8(C2^2xD7)448,1200
C8.9(C22×D7) = C56.9C23φ: C22×D7/C14C22 ⊆ Aut C81124C8.9(C2^2xD7)448,1201
C8.10(C22×D7) = D813D14φ: C22×D7/C14C22 ⊆ Aut C81124C8.10(C2^2xD7)448,1210
C8.11(C22×D7) = C2×SD16⋊D7φ: C22×D7/C14C22 ⊆ Aut C8224C8.11(C2^2xD7)448,1213
C8.12(C22×D7) = D28.29D4φ: C22×D7/C14C22 ⊆ Aut C81124C8.12(C2^2xD7)448,1215
C8.13(C22×D7) = C2×Q16⋊D7φ: C22×D7/C14C22 ⊆ Aut C8224C8.13(C2^2xD7)448,1217
C8.14(C22×D7) = D28.30D4φ: C22×D7/C14C22 ⊆ Aut C82244C8.14(C2^2xD7)448,1219
C8.15(C22×D7) = D810D14φ: C22×D7/C14C22 ⊆ Aut C81124C8.15(C2^2xD7)448,1221
C8.16(C22×D7) = D815D14φ: C22×D7/C14C22 ⊆ Aut C81124+C8.16(C2^2xD7)448,1222
C8.17(C22×D7) = D811D14φ: C22×D7/C14C22 ⊆ Aut C81124C8.17(C2^2xD7)448,1223
C8.18(C22×D7) = D8.10D14φ: C22×D7/C14C22 ⊆ Aut C82244-C8.18(C2^2xD7)448,1224
C8.19(C22×D7) = D7×D16φ: C22×D7/D14C2 ⊆ Aut C81124+C8.19(C2^2xD7)448,444
C8.20(C22×D7) = D8⋊D14φ: C22×D7/D14C2 ⊆ Aut C81124C8.20(C2^2xD7)448,445
C8.21(C22×D7) = D163D7φ: C22×D7/D14C2 ⊆ Aut C82244-C8.21(C2^2xD7)448,446
C8.22(C22×D7) = D7×SD32φ: C22×D7/D14C2 ⊆ Aut C81124C8.22(C2^2xD7)448,447
C8.23(C22×D7) = D112⋊C2φ: C22×D7/D14C2 ⊆ Aut C81124+C8.23(C2^2xD7)448,448
C8.24(C22×D7) = SD32⋊D7φ: C22×D7/D14C2 ⊆ Aut C82244-C8.24(C2^2xD7)448,449
C8.25(C22×D7) = SD323D7φ: C22×D7/D14C2 ⊆ Aut C82244C8.25(C2^2xD7)448,450
C8.26(C22×D7) = D7×Q32φ: C22×D7/D14C2 ⊆ Aut C82244-C8.26(C2^2xD7)448,451
C8.27(C22×D7) = Q32⋊D7φ: C22×D7/D14C2 ⊆ Aut C82244C8.27(C2^2xD7)448,452
C8.28(C22×D7) = Q323D7φ: C22×D7/D14C2 ⊆ Aut C82244+C8.28(C2^2xD7)448,453
C8.29(C22×D7) = C2×C7⋊D16φ: C22×D7/D14C2 ⊆ Aut C8224C8.29(C2^2xD7)448,680
C8.30(C22×D7) = D8.D14φ: C22×D7/D14C2 ⊆ Aut C81124C8.30(C2^2xD7)448,681
C8.31(C22×D7) = C2×D8.D7φ: C22×D7/D14C2 ⊆ Aut C8224C8.31(C2^2xD7)448,682
C8.32(C22×D7) = C2×C7⋊SD32φ: C22×D7/D14C2 ⊆ Aut C8224C8.32(C2^2xD7)448,712
C8.33(C22×D7) = Q16.D14φ: C22×D7/D14C2 ⊆ Aut C82244C8.33(C2^2xD7)448,713
C8.34(C22×D7) = C2×C7⋊Q32φ: C22×D7/D14C2 ⊆ Aut C8448C8.34(C2^2xD7)448,714
C8.35(C22×D7) = Q16⋊D14φ: C22×D7/D14C2 ⊆ Aut C81124+C8.35(C2^2xD7)448,727
C8.36(C22×D7) = C56.30C23φ: C22×D7/D14C2 ⊆ Aut C82244C8.36(C2^2xD7)448,728
C8.37(C22×D7) = C56.31C23φ: C22×D7/D14C2 ⊆ Aut C82244-C8.37(C2^2xD7)448,729
C8.38(C22×D7) = C2×D83D7φ: C22×D7/D14C2 ⊆ Aut C8224C8.38(C2^2xD7)448,1209
C8.39(C22×D7) = C2×D7×Q16φ: C22×D7/D14C2 ⊆ Aut C8224C8.39(C2^2xD7)448,1216
C8.40(C22×D7) = C2×Q8.D14φ: C22×D7/D14C2 ⊆ Aut C8224C8.40(C2^2xD7)448,1218
C8.41(C22×D7) = C2×SD163D7φ: C22×D7/D14C2 ⊆ Aut C8224C8.41(C2^2xD7)448,1214
C8.42(C22×D7) = D7×C4○D8φ: C22×D7/D14C2 ⊆ Aut C81124C8.42(C2^2xD7)448,1220
C8.43(C22×D7) = C2×D28.C4φ: C22×D7/D14C2 ⊆ Aut C8224C8.43(C2^2xD7)448,1197
C8.44(C22×D7) = C28.70C24φ: C22×D7/D14C2 ⊆ Aut C81124C8.44(C2^2xD7)448,1198
C8.45(C22×D7) = C2×D112φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8.45(C2^2xD7)448,436
C8.46(C22×D7) = C2×C112⋊C2φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8.46(C2^2xD7)448,437
C8.47(C22×D7) = D1127C2φ: C22×D7/C2×C14C2 ⊆ Aut C82242C8.47(C2^2xD7)448,438
C8.48(C22×D7) = C2×Dic56φ: C22×D7/C2×C14C2 ⊆ Aut C8448C8.48(C2^2xD7)448,439
C8.49(C22×D7) = C16⋊D14φ: C22×D7/C2×C14C2 ⊆ Aut C81124+C8.49(C2^2xD7)448,442
C8.50(C22×D7) = C16.D14φ: C22×D7/C2×C14C2 ⊆ Aut C82244-C8.50(C2^2xD7)448,443
C8.51(C22×D7) = C2×D567C2φ: C22×D7/C2×C14C2 ⊆ Aut C8224C8.51(C2^2xD7)448,1194
C8.52(C22×D7) = C22×Dic28φ: C22×D7/C2×C14C2 ⊆ Aut C8448C8.52(C2^2xD7)448,1195
C8.53(C22×D7) = D4.12D28φ: C22×D7/C2×C14C2 ⊆ Aut C81124+C8.53(C2^2xD7)448,1205
C8.54(C22×D7) = D4.13D28φ: C22×D7/C2×C14C2 ⊆ Aut C82244-C8.54(C2^2xD7)448,1206
C8.55(C22×D7) = D4.11D28φ: C22×D7/C2×C14C2 ⊆ Aut C81124C8.55(C2^2xD7)448,1204
C8.56(C22×D7) = C56.49C23φ: C22×D7/C2×C14C2 ⊆ Aut C81124C8.56(C2^2xD7)448,1203
C8.57(C22×D7) = D7×C2×C16central extension (φ=1)224C8.57(C2^2xD7)448,433
C8.58(C22×D7) = C2×C16⋊D7central extension (φ=1)224C8.58(C2^2xD7)448,434
C8.59(C22×D7) = D28.4C8central extension (φ=1)2242C8.59(C2^2xD7)448,435
C8.60(C22×D7) = D7×M5(2)central extension (φ=1)1124C8.60(C2^2xD7)448,440
C8.61(C22×D7) = C16.12D14central extension (φ=1)2244C8.61(C2^2xD7)448,441
C8.62(C22×D7) = C22×C7⋊C16central extension (φ=1)448C8.62(C2^2xD7)448,630
C8.63(C22×D7) = C2×C28.C8central extension (φ=1)224C8.63(C2^2xD7)448,631
C8.64(C22×D7) = C56.70C23central extension (φ=1)2244C8.64(C2^2xD7)448,674
C8.65(C22×D7) = C2×D28.2C4central extension (φ=1)224C8.65(C2^2xD7)448,1191
C8.66(C22×D7) = D7×C8○D4central extension (φ=1)1124C8.66(C2^2xD7)448,1202

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