# Extensions 1→N→G→Q→1 with N=C23 and Q=C22×C6

Direct product G=N×Q with N=C23 and Q=C22×C6
dρLabelID
C25×C6192C2^5xC6192,1543

Semidirect products G=N:Q with N=C23 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C231(C22×C6) = C6×C22≀C2φ: C22×C6/C6C22 ⊆ Aut C2348C2^3:1(C2^2xC6)192,1410
C232(C22×C6) = C6×2+ 1+4φ: C22×C6/C6C22 ⊆ Aut C2348C2^3:2(C2^2xC6)192,1534
C233(C22×C6) = A4×C24φ: C22×C6/C23C3 ⊆ Aut C2348C2^3:3(C2^2xC6)192,1539
C234(C22×C6) = D4×C22×C6φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3:4(C2^2xC6)192,1531

Non-split extensions G=N.Q with N=C23 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C23.1(C22×C6) = C6×C23⋊C4φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.1(C2^2xC6)192,842
C23.2(C22×C6) = C3×C23.C23φ: C22×C6/C6C22 ⊆ Aut C23484C2^3.2(C2^2xC6)192,843
C23.3(C22×C6) = C3×C2≀C22φ: C22×C6/C6C22 ⊆ Aut C23244C2^3.3(C2^2xC6)192,890
C23.4(C22×C6) = C3×C23.7D4φ: C22×C6/C6C22 ⊆ Aut C23484C2^3.4(C2^2xC6)192,891
C23.5(C22×C6) = C6×C22.D4φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.5(C2^2xC6)192,1413
C23.6(C22×C6) = C6×C4.4D4φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.6(C2^2xC6)192,1415
C23.7(C22×C6) = C3×C23.36C23φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.7(C2^2xC6)192,1418
C23.8(C22×C6) = C6×C41D4φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.8(C2^2xC6)192,1419
C23.9(C22×C6) = C3×C22.29C24φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.9(C2^2xC6)192,1424
C23.10(C22×C6) = C3×C23.38C23φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.10(C2^2xC6)192,1425
C23.11(C22×C6) = C3×C22.32C24φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.11(C2^2xC6)192,1427
C23.12(C22×C6) = C3×C22.34C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.12(C2^2xC6)192,1429
C23.13(C22×C6) = C3×C22.35C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.13(C2^2xC6)192,1430
C23.14(C22×C6) = C3×C22.36C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.14(C2^2xC6)192,1431
C23.15(C22×C6) = C3×D42φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.15(C2^2xC6)192,1434
C23.16(C22×C6) = C3×D45D4φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.16(C2^2xC6)192,1435
C23.17(C22×C6) = C3×Q86D4φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.17(C2^2xC6)192,1439
C23.18(C22×C6) = C3×C22.45C24φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.18(C2^2xC6)192,1440
C23.19(C22×C6) = C3×C22.47C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.19(C2^2xC6)192,1442
C23.20(C22×C6) = C3×C22.49C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.20(C2^2xC6)192,1444
C23.21(C22×C6) = C3×C22.50C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.21(C2^2xC6)192,1445
C23.22(C22×C6) = C3×C22.53C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.22(C2^2xC6)192,1448
C23.23(C22×C6) = C3×C22.54C24φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.23(C2^2xC6)192,1449
C23.24(C22×C6) = C3×C24⋊C22φ: C22×C6/C6C22 ⊆ Aut C2348C2^3.24(C2^2xC6)192,1450
C23.25(C22×C6) = C3×C22.56C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.25(C2^2xC6)192,1451
C23.26(C22×C6) = C3×C22.57C24φ: C22×C6/C6C22 ⊆ Aut C2396C2^3.26(C2^2xC6)192,1452
C23.27(C22×C6) = C3×C2.C25φ: C22×C6/C6C22 ⊆ Aut C23484C2^3.27(C2^2xC6)192,1536
C23.28(C22×C6) = A4×C22×C4φ: C22×C6/C23C3 ⊆ Aut C2348C2^3.28(C2^2xC6)192,1496
C23.29(C22×C6) = C2×D4×A4φ: C22×C6/C23C3 ⊆ Aut C2324C2^3.29(C2^2xC6)192,1497
C23.30(C22×C6) = C2×Q8×A4φ: C22×C6/C23C3 ⊆ Aut C2348C2^3.30(C2^2xC6)192,1499
C23.31(C22×C6) = A4×C4○D4φ: C22×C6/C23C3 ⊆ Aut C23246C2^3.31(C2^2xC6)192,1501
C23.32(C22×C6) = D4×C2×C12φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.32(C2^2xC6)192,1404
C23.33(C22×C6) = C12×C4○D4φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.33(C2^2xC6)192,1406
C23.34(C22×C6) = C3×C22.11C24φ: C22×C6/C2×C6C2 ⊆ Aut C2348C2^3.34(C2^2xC6)192,1407
C23.35(C22×C6) = C3×C23.32C23φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.35(C2^2xC6)192,1408
C23.36(C22×C6) = C3×C23.33C23φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.36(C2^2xC6)192,1409
C23.37(C22×C6) = C3×C22.19C24φ: C22×C6/C2×C6C2 ⊆ Aut C2348C2^3.37(C2^2xC6)192,1414
C23.38(C22×C6) = C3×C22.26C24φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.38(C2^2xC6)192,1421
C23.39(C22×C6) = C3×C23.37C23φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.39(C2^2xC6)192,1422
C23.40(C22×C6) = C3×C233D4φ: C22×C6/C2×C6C2 ⊆ Aut C2348C2^3.40(C2^2xC6)192,1423
C23.41(C22×C6) = C3×C22.31C24φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.41(C2^2xC6)192,1426
C23.42(C22×C6) = C3×C22.33C24φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.42(C2^2xC6)192,1428
C23.43(C22×C6) = C3×C232Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2348C2^3.43(C2^2xC6)192,1432
C23.44(C22×C6) = C3×C23.41C23φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.44(C2^2xC6)192,1433
C23.45(C22×C6) = C3×D46D4φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.45(C2^2xC6)192,1436
C23.46(C22×C6) = C3×Q85D4φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.46(C2^2xC6)192,1437
C23.47(C22×C6) = C3×D4×Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.47(C2^2xC6)192,1438
C23.48(C22×C6) = C3×C22.46C24φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.48(C2^2xC6)192,1441
C23.49(C22×C6) = C3×D43Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.49(C2^2xC6)192,1443
C23.50(C22×C6) = C2×C6×C4○D4φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.50(C2^2xC6)192,1533
C23.51(C22×C6) = C6×2- 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C2396C2^3.51(C2^2xC6)192,1535
C23.52(C22×C6) = C6×C2.C42central extension (φ=1)192C2^3.52(C2^2xC6)192,808
C23.53(C22×C6) = C3×C424C4central extension (φ=1)192C2^3.53(C2^2xC6)192,809
C23.54(C22×C6) = C12×C22⋊C4central extension (φ=1)96C2^3.54(C2^2xC6)192,810
C23.55(C22×C6) = C12×C4⋊C4central extension (φ=1)192C2^3.55(C2^2xC6)192,811
C23.56(C22×C6) = C3×C243C4central extension (φ=1)48C2^3.56(C2^2xC6)192,812
C23.57(C22×C6) = C3×C23.7Q8central extension (φ=1)96C2^3.57(C2^2xC6)192,813
C23.58(C22×C6) = C3×C23.34D4central extension (φ=1)96C2^3.58(C2^2xC6)192,814
C23.59(C22×C6) = C3×C428C4central extension (φ=1)192C2^3.59(C2^2xC6)192,815
C23.60(C22×C6) = C3×C425C4central extension (φ=1)192C2^3.60(C2^2xC6)192,816
C23.61(C22×C6) = C3×C429C4central extension (φ=1)192C2^3.61(C2^2xC6)192,817
C23.62(C22×C6) = C3×C23.8Q8central extension (φ=1)96C2^3.62(C2^2xC6)192,818
C23.63(C22×C6) = C3×C23.23D4central extension (φ=1)96C2^3.63(C2^2xC6)192,819
C23.64(C22×C6) = C3×C23.63C23central extension (φ=1)192C2^3.64(C2^2xC6)192,820
C23.65(C22×C6) = C3×C24.C22central extension (φ=1)96C2^3.65(C2^2xC6)192,821
C23.66(C22×C6) = C3×C23.65C23central extension (φ=1)192C2^3.66(C2^2xC6)192,822
C23.67(C22×C6) = C3×C24.3C22central extension (φ=1)96C2^3.67(C2^2xC6)192,823
C23.68(C22×C6) = C3×C23.67C23central extension (φ=1)192C2^3.68(C2^2xC6)192,824
C23.69(C22×C6) = C2×C6×C22⋊C4central extension (φ=1)96C2^3.69(C2^2xC6)192,1401
C23.70(C22×C6) = C2×C6×C4⋊C4central extension (φ=1)192C2^3.70(C2^2xC6)192,1402
C23.71(C22×C6) = C6×C42⋊C2central extension (φ=1)96C2^3.71(C2^2xC6)192,1403
C23.72(C22×C6) = Q8×C2×C12central extension (φ=1)192C2^3.72(C2^2xC6)192,1405
C23.73(C22×C6) = C6×C4⋊D4central extension (φ=1)96C2^3.73(C2^2xC6)192,1411
C23.74(C22×C6) = C6×C22⋊Q8central extension (φ=1)96C2^3.74(C2^2xC6)192,1412
C23.75(C22×C6) = C6×C42.C2central extension (φ=1)192C2^3.75(C2^2xC6)192,1416
C23.76(C22×C6) = C6×C422C2central extension (φ=1)96C2^3.76(C2^2xC6)192,1417
C23.77(C22×C6) = C6×C4⋊Q8central extension (φ=1)192C2^3.77(C2^2xC6)192,1420
C23.78(C22×C6) = Q8×C22×C6central extension (φ=1)192C2^3.78(C2^2xC6)192,1532
C23.79(C22×C6) = C3×C232D4central stem extension (φ=1)96C2^3.79(C2^2xC6)192,825
C23.80(C22×C6) = C3×C23⋊Q8central stem extension (φ=1)96C2^3.80(C2^2xC6)192,826
C23.81(C22×C6) = C3×C23.10D4central stem extension (φ=1)96C2^3.81(C2^2xC6)192,827
C23.82(C22×C6) = C3×C23.78C23central stem extension (φ=1)192C2^3.82(C2^2xC6)192,828
C23.83(C22×C6) = C3×C23.Q8central stem extension (φ=1)96C2^3.83(C2^2xC6)192,829
C23.84(C22×C6) = C3×C23.11D4central stem extension (φ=1)96C2^3.84(C2^2xC6)192,830
C23.85(C22×C6) = C3×C23.81C23central stem extension (φ=1)192C2^3.85(C2^2xC6)192,831
C23.86(C22×C6) = C3×C23.4Q8central stem extension (φ=1)96C2^3.86(C2^2xC6)192,832
C23.87(C22×C6) = C3×C23.83C23central stem extension (φ=1)192C2^3.87(C2^2xC6)192,833
C23.88(C22×C6) = C3×C23.84C23central stem extension (φ=1)192C2^3.88(C2^2xC6)192,834

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