Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
986 conjugacy classes of subgroups; only the 472 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 472 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 |
|---|---|---|
| 2. C9×#11719687 | C3 | semidirect |
| 3. C9×#11719686 | C3 | semidirect |
| 4. C9×#11719689 | C3 | semidirect |
| 6. #21419296 | C3 | semidirect |
| 7. #21419294 | C3 | semidirect |
| 8. C92×C31⋊C3 | C3 | semidirect |
| 9. C3×C92×C31 | C3 | semidirect |
| 10. #14578912 | C9 | direct (N × H) |
| 33. C3×C9×C31 | C3×C9 | semidirect |
| 40. #11719689 | C3×C9 | semidirect |
| 43. #11719687 | C3×C9 | semidirect |
| 44. #11719686 | C3×C9 | semidirect |
| 46. C9×C31⋊C3 | C3×C9 | semidirect |
| 57. C9×C31 | #737 | semidirect |
| 68. C3×C92 | C31⋊C3 | semidirect |
| 93. C31 | C9×#737 | semidirect |
| 105. C3×C9 | C9×C31⋊C3 | semidirect |
| 122. C9 | #14578912 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| C9×#11719687 | 3 |
| C9×#11719686 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| #21419296 | 3 |
| #21419294 | 3 |
| C92×C31⋊C3 | 3 |
| C3×C92×C31 | 3 |
| C9×#737 | 31 |