Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 454 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. #21419306 | C3 | semidirect |
| 3. C9×#11719686 | C3 | semidirect |
| 4. #11719687⋊C9 | C3 | semidirect |
| 6. #21419296 | C3 | semidirect |
| 7. #21419295 | C3 | semidirect |
| 8. C3×#14578886 | C3 | semidirect |
| 9. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 10. C31×#6887 | C3 | semidirect |
| 11. #14578912 | C9 | semidirect |
| 38. C3×C9×C31 | C3×C9 | semidirect |
| 44. #11719689 | C3×C9 | semidirect |
| 50. #11719687 | C3×C9 | semidirect |
| 51. #11719686 | C3×C9 | semidirect |
| 53. C9×C31⋊C3 | C3×C9 | semidirect |
| 75. #6887 | C31⋊C3 | semidirect |
| 107. C31 | #10624864 | semidirect |
| 121. C3×C9 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419306 | 3 |
| C9×#11719686 | 3 |
| #11719687⋊C9 | 3 |
| #21419297 | 3 |
| #21419296 | 3 |
| #21419295 | 3 |
| C3×#14578886 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| C31×#6887 | 3 |
| #10624864 | 31 |