Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
948 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 286 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. #21419437 | C3 | semidirect |
| 2. C3×#14578913 | C3 | semidirect |
| 3. #21419414 | C3 | semidirect |
| 4. #21419413 | C3 | semidirect |
| 5. #21419409 | C3 | semidirect |
| 6. #21419405 | C3 | semidirect |
| 7. #21419397 | C3 | semidirect |
| 8. #21419395 | C3 | semidirect |
| 9. #21419388 | C3 | semidirect |
| 10. C3×#14578898 | C3 | semidirect |
| 11. C3×#14578896 | C3 | semidirect |
| 12. C31×3−1+4 | C3 | semidirect |
| 17. #14578912 | C32 | semidirect |
| 21. C3×#11719686 | C32 | semidirect |
| 22. C3×#11719687 | C32 | semidirect |
| 27. C3×C9×C31⋊C3 | C32 | semidirect |
| 28. #14578901 | C32 | semidirect |
| 30. #14578898 | C32 | semidirect |
| 31. #14578898 | C32 | semidirect |
| 32. #14578898 | C32 | semidirect |
| 33. #14578896 | C32 | semidirect |
| 34. #14578896 | C32 | semidirect |
| 35. #14578896 | C32 | semidirect |
| 36. #14578895 | C32 | semidirect |
| 37. #14578893 | C32 | semidirect |
| 39. C31×#737 | C32 | semidirect |
| 106. 3−1+4 | C31⋊C3 | semidirect |
| 130. #737 | C3×C31⋊C3 | semidirect |
| 155. C31 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| C3×#14578913 | 3 |
| #21419414 | 3 |
| #21419413 | 3 |
| #21419409 | 3 |
| #21419405 | 3 |
| #21419397 | 3 |
| #21419395 | 3 |
| #21419388 | 3 |
| C3×#14578898 | 3 |
| C3×#14578896 | 3 |
| C31×3−1+4 | 3 |
| #10624935 | 31 |