Order 36036.
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C13×D77 | C2 | semidirect |
| 2. C9×C11×C13×D7 | C2 | semidirect |
| 3. C7×C9×C13×D11 | C2 | semidirect |
| 5. C7×C9×C11×C13 | C22 | semidirect |
| 10. C13×D7×D11 | C9 | direct (N × H) |
| 13. C9×D7×D11 | C13 | direct (N × H) |
| 15. C9×C13×D11 | D7 | direct (N × H) |
| 17. C13×D77 | C2×C9 | semidirect |
| 18. C11×C13×D7 | C2×C9 | semidirect |
| 19. C7×C13×D11 | C2×C9 | semidirect |
| 23. C9×C13×D7 | D11 | direct (N × H) |
| 24. C9×D77 | C2×C13 | semidirect |
| 25. C9×C11×D7 | C2×C13 | semidirect |
| 26. C7×C9×D11 | C2×C13 | semidirect |
| 27. C9×C11×C13 | C2×D7 | semidirect |
| 29. C7×C11×C13 | C22×C9 | semidirect |
| 34. C7×C9×C13 | C2×D11 | semidirect |
| 35. C7×C9×C11 | C22×C13 | semidirect |
| 47. D7×D11 | C9×C13 | direct (N × H) |
| 50. C13×D11 | C9×D7 | direct (N × H) |
| 59. C9×D11 | C13×D7 | direct (N × H) |
| 62. C13×D7 | C9×D11 | direct (N × H) |
| 64. D77 | C2×C9×C13 | semidirect |
| 65. C7×D11 | C2×C9×C13 | semidirect |
| 66. C11×D7 | C2×C9×C13 | semidirect |
| 67. C11×C13 | C2×C9×D7 | semidirect |
| 71. C9×D7 | C13×D11 | direct (N × H) |
| 72. C9×C13 | D7×D11 | direct (N × H) |
| 73. C9×C11 | C2×C13×D7 | semidirect |
| 74. C7×C13 | C2×C9×D11 | semidirect |
| 79. C7×C11 | C22×C9×C13 | semidirect |
| 83. C7×C9 | C2×C13×D11 | semidirect |
| 98. D11 | C9×C13×D7 | direct (N × H) |
| 105. D7 | C9×C13×D11 | direct (N × H) |
| 106. C13 | C9×D7×D11 | direct (N × H) |
| 108. C11 | C2×C9×C13×D7 | semidirect |
| 109. C9 | C13×D7×D11 | direct (N × H) |
| 110. C7 | C2×C9×C13×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C13×D77 | 2 |
| C9×C11×C13×D7 | 2 |
| C7×C9×C13×D11 | 2 |
| C3×C13×D7×D11 | 3 |
| C2×C9×C13×D11 | 7 |
| C2×C9×C13×D7 | 11 |
| C9×D7×D11 | 13 |