Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
472 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 82 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. C33×C31⋊C9 | C3 | semidirect |
| 3. #21419306 | C3 | semidirect |
| 4. #21419297 | C3 | semidirect |
| 5. #21419239 | C3 | semidirect |
| 6. #21419236 | C3 | semidirect |
| 7. #21419233 | C3 | semidirect |
| 8. #21419226 | C3 | semidirect |
| 9. C31×#6866 | C3 | semidirect |
| 18. #14578894 | C9 | semidirect |
| 31. C33×C31 | C3×C9 | semidirect |
| 37. C32⋊(C31⋊C3) | C3×C9 | semidirect |
| 39. #11719689 | C3×C9 | semidirect |
| 72. C31⋊C9 | AΣL(1,𝔽27) | semidirect |
| 81. #6866 | C31⋊C3 | semidirect |
| 106. C31 | C9×AΣL(1,𝔽27) | semidirect |
| 112. C33 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C31⋊C9 | 3 |
| C3×#14578894 | 3 |
| #21419306 | 3 |
| #21419297 | 3 |
| #21419239 | 3 |
| #21419236 | 3 |
| #21419233 | 3 |
| #21419226 | 3 |
| C31×#6866 | 3 |
| C9×AΣL(1,𝔽27) | 31 |