Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
944 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 454 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 |
|---|---|---|
| 2. C9×#11719686 | C3 | semidirect |
| 3. #11719686⋊C9 | C3 | semidirect |
| 4. #21419296 | C3 | semidirect |
| 5. #21419293 | C3 | semidirect |
| 7. C31×#6887 | C3 | semidirect |
| 9. C3×#11719686 | C9 | semidirect |
| 14. #14578887 | C32 | semidirect |
| 15. #14578886 | C32 | semidirect |
| 16. (C31⋊C9)⋊C9 | C32 | semidirect |
| 19. C9×C31⋊C9 | C32 | semidirect |
| 20. C9×C31⋊C9 | C32 | semidirect |
| 22. C31×C9⋊C9 | C32 | semidirect |
| 24. C92×C31 | C32 | semidirect |
| 29. C3×C9×C31 | C3×C9 | semidirect |
| 33. C3×C31⋊C9 | C3×C9 | semidirect |
| 36. #11719686 | C3×C9 | semidirect |
| 37. #11719686 | C3×C9 | semidirect |
| 57. #6887 | C31⋊C3 | semidirect |
| 73. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 79. C92 | C3×C31⋊C3 | semidirect |
| 80. C31 | #10624863 | semidirect |
| 91. C3×C9 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719686 | 3 |
| C9×#11719686 | 3 |
| #11719686⋊C9 | 3 |
| #21419296 | 3 |
| #21419293 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C31×#6887 | 3 |
| #10624863 | 31 |