Finite Group DatabasebetaFinite Group DatabasebetaOrder 36036.
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C9×C11×C13 | C22 |
| Frattini | C3 | D33×D91 |
| socle | C3×C7×C11×C13 | C2×D3 |
| LCS | G ▷ C7×C9×C11×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D9009 | C2 | semidirect |
| 2. C7×C13×D99 | C2 | semidirect |
| 3. C9×C11×D91 | C2 | semidirect |
| 5. C7×C9×C11×C13 | C22 | semidirect |
| 15. C13×D99 | D7 | semidirect |
| 18. C11×D91 | D9 | semidirect |
| 23. C9×D91 | D11 | semidirect |
| 25. C7×D99 | D13 | semidirect |
| 27. C9×C11×C13 | C2×D7 | semidirect |
| 29. C7×C11×C13 | C2×D9 | semidirect |
| 34. C7×C9×C13 | C2×D11 | semidirect |
| 35. C7×C9×C11 | C2×D13 | semidirect |
| 59. D99 | D91 | direct (N × H) |
| 62. D91 | D99 | direct (N × H) |
| 67. C11×C13 | D7×D9 | semidirect |
| 72. C9×C13 | D7×D11 | semidirect |
| 73. C9×C11 | C2×D91 | semidirect |
| 74. C7×C13 | C2×D99 | semidirect |
| 79. C7×C11 | D9×D13 | semidirect |
| 83. C7×C9 | D11×D13 | semidirect |
| 106. C13 | D7×D99 | semidirect |
| 108. C11 | D9×D91 | semidirect |
| 109. C9 | D11×D91 | semidirect |
| 110. C7 | D13×D99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9009 | 2 |
| C7×C13×D99 | 2 |
| C9×C11×D91 | 2 |
| D33×D91 | 3 |
| D13×D99 | 7 |
| D9×D91 | 11 |
| D7×D99 | 13 |