Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
824 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 310 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. #21419336 | C3 | semidirect |
| 2. #21419330 | C3 | semidirect |
| 3. #21419329 | C3 | semidirect |
| 5. C9×#11719689 | C3 | semidirect |
| 6. #21419296 | C3 | semidirect |
| 9. #14578887 | C32 | semidirect |
| 10. #14578886 | C32 | semidirect |
| 11. (C31⋊C9)⋊C9 | C32 | semidirect |
| 14. C9×C31⋊C9 | C32 | semidirect |
| 30. C3×C9×C31 | 3−1+2 | semidirect |
| 75. C31 | #10624872 | semidirect |
| 86. C3×C9 | #11719689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419336 | 3 |
| #21419330 | 3 |
| #21419329 | 3 |
| #21419312 | 3 |
| C9×#11719689 | 3 |
| #21419296 | 3 |
| C33×C9×C31 | 3 |
| #10624872 | 31 |