Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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. #21419419 | C3 | semidirect |
| 2. #21419406 | C3 | semidirect |
| 3. #21419359 | C3 | semidirect |
| 4. #21419280 | C3 | semidirect |
| 5. #21419279 | C3 | semidirect |
| 6. #21419273 | C3 | semidirect |
| 7. #21419272 | C3 | semidirect |
| 8. #21419270 | C3 | semidirect |
| 9. #21419269 | C3 | semidirect |
| 10. #21419264 | C3 | semidirect |
| 11. #21419263 | C3 | semidirect |
| 12. #21419262 | C3 | semidirect |
| 13. C31×#6913 | C3 | semidirect |
| 17. #14578902 | C32 | semidirect |
| 18. #14578902 | C32 | semidirect |
| 24. #14578900 | C32 | semidirect |
| 27. #14578887 | C32 | semidirect |
| 28. #14578886 | C32 | semidirect |
| 31. C9×C31⋊C9 | C32 | semidirect |
| 34. C31×#733 | C32 | semidirect |
| 35. C31×#733 | C32 | semidirect |
| 36. C31×#732 | C32 | semidirect |
| 85. #6913 | C31⋊C3 | semidirect |
| 112. #733 | C3×C31⋊C3 | semidirect |
| 113. #733 | C3×C31⋊C3 | semidirect |
| 120. #732 | C3×C31⋊C3 | semidirect |
| 130. C31 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419419 | 3 |
| #21419406 | 3 |
| #21419359 | 3 |
| #21419280 | 3 |
| #21419279 | 3 |
| #21419273 | 3 |
| #21419272 | 3 |
| #21419270 | 3 |
| #21419269 | 3 |
| #21419264 | 3 |
| #21419263 | 3 |
| #21419262 | 3 |
| C31×#6913 | 3 |
| #10624851 | 31 |