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×#14578911 | C3 | semidirect |
| 4. #21419412 | C3 | semidirect |
| 5. #21419411 | C3 | semidirect |
| 6. #21419409 | C3 | semidirect |
| 7. #21419405 | C3 | semidirect |
| 8. #21419396 | C3 | semidirect |
| 9. #21419387 | C3 | semidirect |
| 10. C3×#14578898 | C3 | semidirect |
| 11. C3×#14578896 | C3 | semidirect |
| 12. C31×#6909 | C3 | semidirect |
| 14. #14578913 | C32 | semidirect |
| 19. #14578911 | C32 | semidirect |
| 25. C3×#11719689 | C32 | semidirect |
| 26. C3×#11719689 | C32 | semidirect |
| 30. C32×C31⋊C9 | C32 | semidirect |
| 31. #14578901 | C32 | semidirect |
| 33. #14578898 | C32 | semidirect |
| 34. #14578898 | C32 | semidirect |
| 35. #14578898 | C32 | semidirect |
| 36. #14578896 | C32 | semidirect |
| 37. #14578896 | C32 | semidirect |
| 38. #14578896 | C32 | semidirect |
| 39. #14578894 | C32 | semidirect |
| 43. C31×AΣL(1,𝔽27) | C32 | semidirect |
| 113. #6909 | C31⋊C3 | semidirect |
| 154. AΣL(1,𝔽27) | 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 |
|---|---|
| #21419438 | 3 |
| #21419437 | 3 |
| C3×#14578911 | 3 |
| #21419412 | 3 |
| #21419411 | 3 |
| #21419409 | 3 |
| #21419405 | 3 |
| #21419396 | 3 |
| #21419387 | 3 |
| C3×#14578898 | 3 |
| C3×#14578896 | 3 |
| C31×#6909 | 3 |
| #10624935 | 31 |