# Extensions 1→N→G→Q→1 with N=C6 and Q=C23×C4

Direct product G=N×Q with N=C6 and Q=C23×C4
dρLabelID
C24×C12192C2^4xC12192,1530

Semidirect products G=N:Q with N=C6 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C61(C23×C4) = S3×C23×C4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6:1(C2^3xC4)192,1511
C62(C23×C4) = Dic3×C24φ: C23×C4/C24C2 ⊆ Aut C6192C6:2(C2^3xC4)192,1528

Non-split extensions G=N.Q with N=C6 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C6.1(C23×C4) = C2×C4×Dic6φ: C23×C4/C22×C4C2 ⊆ Aut C6192C6.1(C2^3xC4)192,1026
C6.2(C23×C4) = S3×C2×C42φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.2(C2^3xC4)192,1030
C6.3(C23×C4) = C2×C422S3φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.3(C2^3xC4)192,1031
C6.4(C23×C4) = C2×C4×D12φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.4(C2^3xC4)192,1032
C6.5(C23×C4) = C4×C4○D12φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.5(C2^3xC4)192,1033
C6.6(C23×C4) = C2×C23.16D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.6(C2^3xC4)192,1039
C6.7(C23×C4) = C2×S3×C22⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.7(C2^3xC4)192,1043
C6.8(C23×C4) = C2×Dic34D4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.8(C2^3xC4)192,1044
C6.9(C23×C4) = C24.35D6φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.9(C2^3xC4)192,1045
C6.10(C23×C4) = C2×Dic6⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C6192C6.10(C2^3xC4)192,1055
C6.11(C23×C4) = C2×S3×C4⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.11(C2^3xC4)192,1060
C6.12(C23×C4) = C2×C4⋊C47S3φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.12(C2^3xC4)192,1061
C6.13(C23×C4) = C2×Dic35D4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.13(C2^3xC4)192,1062
C6.14(C23×C4) = C6.82+ 1+4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.14(C2^3xC4)192,1063
C6.15(C23×C4) = C42.87D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.15(C2^3xC4)192,1075
C6.16(C23×C4) = S3×C42⋊C2φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.16(C2^3xC4)192,1079
C6.17(C23×C4) = C429D6φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.17(C2^3xC4)192,1080
C6.18(C23×C4) = C42.188D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.18(C2^3xC4)192,1081
C6.19(C23×C4) = C42.91D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.19(C2^3xC4)192,1082
C6.20(C23×C4) = C4×D42S3φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.20(C2^3xC4)192,1095
C6.21(C23×C4) = C4×S3×D4φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.21(C2^3xC4)192,1103
C6.22(C23×C4) = C4213D6φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.22(C2^3xC4)192,1104
C6.23(C23×C4) = C42.108D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.23(C2^3xC4)192,1105
C6.24(C23×C4) = C4×S3×Q8φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.24(C2^3xC4)192,1130
C6.25(C23×C4) = C42.125D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.25(C2^3xC4)192,1131
C6.26(C23×C4) = C4×Q83S3φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.26(C2^3xC4)192,1132
C6.27(C23×C4) = C42.126D6φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.27(C2^3xC4)192,1133
C6.28(C23×C4) = S3×C22×C8φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.28(C2^3xC4)192,1295
C6.29(C23×C4) = C22×C8⋊S3φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.29(C2^3xC4)192,1296
C6.30(C23×C4) = C2×C8○D12φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.30(C2^3xC4)192,1297
C6.31(C23×C4) = C2×S3×M4(2)φ: C23×C4/C22×C4C2 ⊆ Aut C648C6.31(C2^3xC4)192,1302
C6.32(C23×C4) = C2×D12.C4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.32(C2^3xC4)192,1303
C6.33(C23×C4) = M4(2)⋊26D6φ: C23×C4/C22×C4C2 ⊆ Aut C6484C6.33(C2^3xC4)192,1304
C6.34(C23×C4) = S3×C8○D4φ: C23×C4/C22×C4C2 ⊆ Aut C6484C6.34(C2^3xC4)192,1308
C6.35(C23×C4) = M4(2)⋊28D6φ: C23×C4/C22×C4C2 ⊆ Aut C6484C6.35(C2^3xC4)192,1309
C6.36(C23×C4) = Dic3×C22×C4φ: C23×C4/C22×C4C2 ⊆ Aut C6192C6.36(C2^3xC4)192,1341
C6.37(C23×C4) = C22×Dic3⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C6192C6.37(C2^3xC4)192,1342
C6.38(C23×C4) = C22×D6⋊C4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.38(C2^3xC4)192,1346
C6.39(C23×C4) = C2×C4×C3⋊D4φ: C23×C4/C22×C4C2 ⊆ Aut C696C6.39(C2^3xC4)192,1347
C6.40(C23×C4) = C23×C3⋊C8φ: C23×C4/C24C2 ⊆ Aut C6192C6.40(C2^3xC4)192,1339
C6.41(C23×C4) = C22×C4.Dic3φ: C23×C4/C24C2 ⊆ Aut C696C6.41(C2^3xC4)192,1340
C6.42(C23×C4) = C22×C4⋊Dic3φ: C23×C4/C24C2 ⊆ Aut C6192C6.42(C2^3xC4)192,1344
C6.43(C23×C4) = C2×C23.26D6φ: C23×C4/C24C2 ⊆ Aut C696C6.43(C2^3xC4)192,1345
C6.44(C23×C4) = C2×D4×Dic3φ: C23×C4/C24C2 ⊆ Aut C696C6.44(C2^3xC4)192,1354
C6.45(C23×C4) = C24.49D6φ: C23×C4/C24C2 ⊆ Aut C648C6.45(C2^3xC4)192,1357
C6.46(C23×C4) = C2×Q8×Dic3φ: C23×C4/C24C2 ⊆ Aut C6192C6.46(C2^3xC4)192,1370
C6.47(C23×C4) = C6.422- 1+4φ: C23×C4/C24C2 ⊆ Aut C696C6.47(C2^3xC4)192,1371
C6.48(C23×C4) = C2×D4.Dic3φ: C23×C4/C24C2 ⊆ Aut C696C6.48(C2^3xC4)192,1377
C6.49(C23×C4) = C12.76C24φ: C23×C4/C24C2 ⊆ Aut C6484C6.49(C2^3xC4)192,1378
C6.50(C23×C4) = Dic3×C4○D4φ: C23×C4/C24C2 ⊆ Aut C696C6.50(C2^3xC4)192,1385
C6.51(C23×C4) = C6.1442+ 1+4φ: C23×C4/C24C2 ⊆ Aut C696C6.51(C2^3xC4)192,1386
C6.52(C23×C4) = C22×C6.D4φ: C23×C4/C24C2 ⊆ Aut C696C6.52(C2^3xC4)192,1398
C6.53(C23×C4) = C2×C6×C22⋊C4central extension (φ=1)96C6.53(C2^3xC4)192,1401
C6.54(C23×C4) = C2×C6×C4⋊C4central extension (φ=1)192C6.54(C2^3xC4)192,1402
C6.55(C23×C4) = C6×C42⋊C2central extension (φ=1)96C6.55(C2^3xC4)192,1403
C6.56(C23×C4) = D4×C2×C12central extension (φ=1)96C6.56(C2^3xC4)192,1404
C6.57(C23×C4) = Q8×C2×C12central extension (φ=1)192C6.57(C2^3xC4)192,1405
C6.58(C23×C4) = C12×C4○D4central extension (φ=1)96C6.58(C2^3xC4)192,1406
C6.59(C23×C4) = C3×C22.11C24central extension (φ=1)48C6.59(C2^3xC4)192,1407
C6.60(C23×C4) = C3×C23.32C23central extension (φ=1)96C6.60(C2^3xC4)192,1408
C6.61(C23×C4) = C3×C23.33C23central extension (φ=1)96C6.61(C2^3xC4)192,1409
C6.62(C23×C4) = C2×C6×M4(2)central extension (φ=1)96C6.62(C2^3xC4)192,1455
C6.63(C23×C4) = C6×C8○D4central extension (φ=1)96C6.63(C2^3xC4)192,1456
C6.64(C23×C4) = C3×Q8○M4(2)central extension (φ=1)484C6.64(C2^3xC4)192,1457

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