Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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×D35 | C2 | semidirect |
| 2. C7×C9×D65 | C2 | semidirect |
| 3. C5×C9×D91 | C2 | semidirect |
| 5. C5×C7×C9×C13 | C22 | semidirect |
| 11. D35⋊D13 | C9 | direct (N × H) |
| 12. C9×D91 | D5 | semidirect |
| 17. C9×D65 | D7 | semidirect |
| 21. C13×D35 | C2×C9 | semidirect |
| 22. C7×D65 | C2×C9 | semidirect |
| 23. C5×D91 | C2×C9 | semidirect |
| 24. C7×C9×C13 | C2×D5 | semidirect |
| 26. C9×D35 | D13 | semidirect |
| 29. C5×C9×C13 | C2×D7 | semidirect |
| 34. C5×C7×C13 | C22×C9 | semidirect |
| 40. C5×C7×C9 | C2×D13 | semidirect |
| 51. D91 | C9×D5 | semidirect |
| 57. D65 | C9×D7 | semidirect |
| 63. C9×C13 | D5×D7 | semidirect |
| 65. C7×C13 | C2×C9×D5 | semidirect |
| 73. D35 | C9×D13 | semidirect |
| 76. C5×C13 | C2×C9×D7 | semidirect |
| 77. C7×C9 | D5×D13 | semidirect |
| 80. C5×C9 | D7×D13 | semidirect |
| 86. C5×C7 | C2×C9×D13 | semidirect |
| 103. C13 | C9×D5×D7 | semidirect |
| 108. C9 | D35⋊D13 | direct (N × H) |
| 109. C7 | C9×D5×D13 | semidirect |
| 113. C5 | C9×D7×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C13×D35 | 2 |
| C7×C9×D65 | 2 |
| C5×C9×D91 | 2 |
| C3×D35⋊D13 | 3 |
| C9×D7×D13 | 5 |
| C9×D5×D13 | 7 |
| C9×D5×D7 | 13 |