Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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×#11719689 | C3 | semidirect |
| 4. #21419238 | C3 | semidirect |
| 6. #21419228 | C3 | semidirect |
| 7. C3×C92×C31 | C3 | semidirect |
| 11. #14578897 | C9 | direct (N × H) |
| 29. C3×C9×C31 | C3×C9 | semidirect |
| 35. #11719689 | C3×C9 | semidirect |
| 52. C9×C31 | #731 | semidirect |
| 59. C3×C92 | C31⋊C3 | semidirect |
| 83. C31 | C9×#731 | semidirect |
| 99. C3×C9 | C9×C31⋊C3 | semidirect |
| 116. C9 | #14578897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578897 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| #21419238 | 3 |
| #21419235 | 3 |
| #21419228 | 3 |
| C3×C92×C31 | 3 |
| C9×#731 | 31 |