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 |
| 3. C3×C9×C31⋊C9 | C3 | semidirect |
| 4. #21419239 | C3 | semidirect |
| 6. #21419227 | C3 | semidirect |
| 11. #14578896 | C9 | direct (N × H) |
| 32. #11719689 | C3×C9 | semidirect |
| 39. C3×C31⋊C9 | C3×C9 | semidirect |
| 51. C9×C31 | #731 | semidirect |
| 83. C31 | C9×#731 | semidirect |
| 116. C9 | #14578896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578896 | 3 |
| C9×#11719689 | 3 |
| C3×C9×C31⋊C9 | 3 |
| #21419239 | 3 |
| H(3,𝔽3)⋊(C31⋊C9) | 3 |
| #21419227 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| C9×#731 | 31 |