Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
662 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 268 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. #21419351 | C3 | semidirect |
| 2. #21419348 | C3 | semidirect |
| 3. #21419343 | C3 | semidirect |
| 4. #21419337 | C3 | semidirect |
| 5. #21419334 | C3 | semidirect |
| 6. #21419333 | C3 | semidirect |
| 7. #21419332 | C3 | semidirect |
| 8. #21419331 | C3 | semidirect |
| 11. C9×#11719689 | C3 | semidirect |
| 12. C9×#11719689 | C3 | semidirect |
| 13. #21419296 | C3 | semidirect |
| 14. C3×C9×C31⋊C9 | C3 | semidirect |
| 151. C31 | #10624877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419351 | 3 |
| #21419348 | 3 |
| #21419343 | 3 |
| #21419337 | 3 |
| #21419334 | 3 |
| #21419333 | 3 |
| #21419332 | 3 |
| #21419331 | 3 |
| #21419320 | 3 |
| #21419314 | 3 |
| C9×#11719689 | 3 |
| #21419296 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624877 | 31 |