Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 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. #21419438 | C3 | semidirect |
| 2. #21419437 | C3 | semidirect |
| 3. C3×#14578913 | C3 | semidirect |
| 4. #21419418 | C3 | semidirect |
| 5. #21419417 | C3 | semidirect |
| 6. #21419401 | C3 | semidirect |
| 7. #21419397 | C3 | semidirect |
| 8. #21419395 | C3 | semidirect |
| 9. #21419390 | C3 | semidirect |
| 10. C3×#14578901 | C3 | semidirect |
| 11. C3×#14578899 | C3 | semidirect |
| 12. C31×#6910 | C3 | semidirect |
| 16. #14578913 | C32 | semidirect |
| 19. #14578911 | C32 | semidirect |
| 24. C3×#11719686 | C32 | semidirect |
| 25. C3×#11719687 | C32 | semidirect |
| 30. C3×C9×C31⋊C3 | C32 | semidirect |
| 31. #14578901 | C32 | semidirect |
| 32. #14578901 | C32 | semidirect |
| 33. #14578901 | C32 | semidirect |
| 37. #14578897 | C32 | semidirect |
| 38. #14578895 | C32 | semidirect |
| 39. #14578893 | C32 | semidirect |
| 43. C31×#731 | C32 | semidirect |
| 111. #6910 | C31⋊C3 | semidirect |
| 152. #731 | C3×C31⋊C3 | semidirect |
| 155. C31 | #10624936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419438 | 3 |
| #21419437 | 3 |
| C3×#14578913 | 3 |
| #21419418 | 3 |
| #21419417 | 3 |
| #21419401 | 3 |
| #21419397 | 3 |
| #21419395 | 3 |
| #21419390 | 3 |
| C3×#14578901 | 3 |
| C3×#14578899 | 3 |
| C31×#6910 | 3 |
| #10624936 | 31 |