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Extensions 1→N→G→Q→1 with N=C23 and Q=C4⋊C4

Direct product G=N×Q with N=C23 and Q=C4⋊C4
dρLabelID
C23×C4⋊C4128C2^3xC4:C4128,2152

Semidirect products G=N:Q with N=C23 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C23⋊(C4⋊C4) = C24.22D4φ: C4⋊C4/C2 → D4 ⊆ Aut C2332C2^3:(C4:C4)128,599
C23⋊2(C4⋊C4) = C24.167C23φ: C4⋊C4/C4 → C4 ⊆ Aut C2332C2^3:2(C4:C4)128,531
C23⋊3(C4⋊C4) = C24.5Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3:3(C4:C4)128,171
C23⋊4(C4⋊C4) = C24.91D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3:4(C4:C4)128,1047
C23⋊5(C4⋊C4) = C2×C23.7Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3:5(C4:C4)128,1010
C23⋊6(C4⋊C4) = C2×C23.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3:6(C4:C4)128,1018

Non-split extensions G=N.Q with N=C23 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C23.1(C4⋊C4) = C23.3C42φ: C4⋊C4/C2 → D4 ⊆ Aut C23324C2^3.1(C4:C4)128,124
C23.2(C4⋊C4) = C24.6D4φ: C4⋊C4/C2 → D4 ⊆ Aut C2332C2^3.2(C4:C4)128,125
C23.3(C4⋊C4) = (C22×C8)⋊C4φ: C4⋊C4/C2 → D4 ⊆ Aut C23324C2^3.3(C4:C4)128,127
C23.4(C4⋊C4) = C24.21D4φ: C4⋊C4/C2 → D4 ⊆ Aut C2332C2^3.4(C4:C4)128,588
C23.5(C4⋊C4) = M4(2).40D4φ: C4⋊C4/C2 → D4 ⊆ Aut C23324C2^3.5(C4:C4)128,590
C23.6(C4⋊C4) = (C2×D4).Q8φ: C4⋊C4/C2 → D4 ⊆ Aut C23324C2^3.6(C4:C4)128,600
C23.7(C4⋊C4) = C24.5D4φ: C4⋊C4/C4 → C4 ⊆ Aut C2332C2^3.7(C4:C4)128,122
C23.8(C4⋊C4) = C42.96D4φ: C4⋊C4/C4 → C4 ⊆ Aut C2332C2^3.8(C4:C4)128,532
C23.9(C4⋊C4) = (C2×D4).24Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C23324C2^3.9(C4:C4)128,544
C23.10(C4⋊C4) = (C2×C8).103D4φ: C4⋊C4/C4 → C4 ⊆ Aut C23324C2^3.10(C4:C4)128,545
C23.11(C4⋊C4) = C24.46D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.11(C4:C4)128,16
C23.12(C4⋊C4) = C42.23D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.12(C4:C4)128,19
C23.13(C4⋊C4) = C42.26D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.13(C4:C4)128,23
C23.14(C4⋊C4) = C24.48D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.14(C4:C4)128,29
C23.15(C4⋊C4) = C42.388D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.15(C4:C4)128,31
C23.16(C4⋊C4) = C24.4Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2316C2^3.16(C4:C4)128,36
C23.17(C4⋊C4) = C23.C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.17(C4:C4)128,37
C23.18(C4⋊C4) = C23.8C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.18(C4:C4)128,38
C23.19(C4⋊C4) = C8⋊1M4(2)φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.19(C4:C4)128,301
C23.20(C4⋊C4) = C42.Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.20(C4:C4)128,304
C23.21(C4⋊C4) = C42.21Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.21(C4:C4)128,306
C23.22(C4⋊C4) = C24.63D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.22(C4:C4)128,465
C23.23(C4⋊C4) = C24.7Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.23(C4:C4)128,470
C23.24(C4⋊C4) = C23.15C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.24(C4:C4)128,474
C23.25(C4⋊C4) = C42.95D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.25(C4:C4)128,530
C23.26(C4⋊C4) = C24.67D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.26(C4:C4)128,541
C23.27(C4⋊C4) = C24.9Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.27(C4:C4)128,543
C23.28(C4⋊C4) = (C2×C8).195D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.28(C4:C4)128,583
C23.29(C4⋊C4) = C24.71D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2364C2^3.29(C4:C4)128,586
C23.30(C4⋊C4) = C24.10Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.30(C4:C4)128,587
C23.31(C4⋊C4) = C42.257C23φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.31(C4:C4)128,1637
C23.32(C4⋊C4) = C24.100D4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.32(C4:C4)128,1643
C23.33(C4⋊C4) = C2×M4(2).C4φ: C4⋊C4/C22 → C22 ⊆ Aut C2332C2^3.33(C4:C4)128,1647
C23.34(C4⋊C4) = C42.20D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.34(C4:C4)128,7
C23.35(C4⋊C4) = M4(2)⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.35(C4:C4)128,10
C23.36(C4⋊C4) = C23.19C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.36(C4:C4)128,12
C23.37(C4⋊C4) = C23.21C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.37(C4:C4)128,14
C23.38(C4⋊C4) = C23.8D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.38(C4:C4)128,21
C23.39(C4⋊C4) = C42.25D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.39(C4:C4)128,22
C23.40(C4⋊C4) = C42.27D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.40(C4:C4)128,24
C23.41(C4⋊C4) = C24.2Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.41(C4:C4)128,25
C23.42(C4⋊C4) = C23.30D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.42(C4:C4)128,26
C23.43(C4⋊C4) = C24.3Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.43(C4:C4)128,30
C23.44(C4⋊C4) = C42.389D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.44(C4:C4)128,33
C23.45(C4⋊C4) = C42.370D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.45(C4:C4)128,34
C23.46(C4⋊C4) = C24.17Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.46(C4:C4)128,165
C23.47(C4⋊C4) = C42.42Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.47(C4:C4)128,296
C23.48(C4⋊C4) = M4(2)⋊1C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.48(C4:C4)128,297
C23.49(C4⋊C4) = C8⋊8M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.49(C4:C4)128,298
C23.50(C4⋊C4) = C8⋊7M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.50(C4:C4)128,299
C23.51(C4⋊C4) = C42.43Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.51(C4:C4)128,300
C23.52(C4⋊C4) = C42.90D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.52(C4:C4)128,302
C23.53(C4⋊C4) = C42.91D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.53(C4:C4)128,303
C23.54(C4⋊C4) = C42.92D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.54(C4:C4)128,305
C23.55(C4⋊C4) = C23.28C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.55(C4:C4)128,460
C23.56(C4⋊C4) = C23.29C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.56(C4:C4)128,461
C23.57(C4⋊C4) = C2×C4.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.57(C4:C4)128,462
C23.58(C4⋊C4) = C2×C4.10C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.58(C4:C4)128,463
C23.59(C4⋊C4) = C2×C42⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.59(C4:C4)128,464
C23.60(C4⋊C4) = C24.132D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.60(C4:C4)128,467
C23.61(C4⋊C4) = C24.152D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.61(C4:C4)128,468
C23.62(C4⋊C4) = C2×C4.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.62(C4:C4)128,469
C23.63(C4⋊C4) = C2×C23.9D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.63(C4:C4)128,471
C23.64(C4⋊C4) = C2×C22.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.64(C4:C4)128,473
C23.65(C4⋊C4) = C2×M4(2)⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.65(C4:C4)128,475
C23.66(C4⋊C4) = C42.425D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.66(C4:C4)128,529
C23.67(C4⋊C4) = C24.133D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.67(C4:C4)128,539
C23.68(C4⋊C4) = C23.22D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.68(C4:C4)128,540
C23.69(C4⋊C4) = C24.19Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2332C2^3.69(C4:C4)128,542
C23.70(C4⋊C4) = C23.21M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.70(C4:C4)128,582
C23.71(C4⋊C4) = C23.37D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.71(C4:C4)128,584
C23.72(C4⋊C4) = C24.159D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.72(C4:C4)128,585
C23.73(C4⋊C4) = C2×C4⋊M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.73(C4:C4)128,1635
C23.74(C4⋊C4) = C2×C42.6C22φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.74(C4:C4)128,1636
C23.75(C4⋊C4) = C2×C23.25D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.75(C4:C4)128,1641
C23.76(C4⋊C4) = C2×M4(2)⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.76(C4:C4)128,1642
C23.77(C4⋊C4) = C22×C8.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2364C2^3.77(C4:C4)128,1646
C23.78(C4⋊C4) = C42.385D4central extension (φ=1)128C2^3.78(C4:C4)128,9
C23.79(C4⋊C4) = C2×C8⋊2C8central extension (φ=1)128C2^3.79(C4:C4)128,294
C23.80(C4⋊C4) = C2×C8⋊1C8central extension (φ=1)128C2^3.80(C4:C4)128,295
C23.81(C4⋊C4) = C2×C22.7C42central extension (φ=1)128C2^3.81(C4:C4)128,459
C23.82(C4⋊C4) = C2×C22.4Q16central extension (φ=1)128C2^3.82(C4:C4)128,466
C23.83(C4⋊C4) = C22×C2.C42central extension (φ=1)128C2^3.83(C4:C4)128,998
C23.84(C4⋊C4) = C22×C4⋊C8central extension (φ=1)128C2^3.84(C4:C4)128,1634
C23.85(C4⋊C4) = C22×C4.Q8central extension (φ=1)128C2^3.85(C4:C4)128,1639
C23.86(C4⋊C4) = C22×C2.D8central extension (φ=1)128C2^3.86(C4:C4)128,1640

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