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. C3×#14578912 | C3 | semidirect |
| 3. #21419416 | C3 | semidirect |
| 4. #21419415 | C3 | semidirect |
| 5. #21419400 | C3 | semidirect |
| 6. #21419395 | C3 | semidirect |
| 7. #21419389 | C3 | semidirect |
| 8. C3×#14578902 | C3 | semidirect |
| 9. C3×C31×#732 | C3 | semidirect |
| 13. #14578911 | C32 | semidirect |
| 18. C3×#11719686 | C32 | semidirect |
| 19. C3×#11719687 | C32 | semidirect |
| 21. C3×C9×C31⋊C3 | C32 | semidirect |
| 22. #14578902 | C32 | semidirect |
| 23. #14578902 | C32 | semidirect |
| 24. #14578902 | C32 | semidirect |
| 25. #14578896 | C32 | semidirect |
| 26. #14578893 | C32 | semidirect |
| 82. C3×#732 | C31⋊C3 | semidirect |
| 111. C31 | #10624936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419438 | 3 |
| C3×#14578912 | 3 |
| #21419416 | 3 |
| #21419415 | 3 |
| #21419400 | 3 |
| #21419395 | 3 |
| #21419389 | 3 |
| C3×#14578902 | 3 |
| C3×C31×#732 | 3 |
| #10624936 | 31 |