Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
692 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 271 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. #21419347 | C3 | semidirect |
| 2. #21419346 | C3 | semidirect |
| 3. #21419345 | C3 | semidirect |
| 4. #21419344 | C3 | semidirect |
| 5. #21419343 | C3 | semidirect |
| 6. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 8. C92×C31⋊C3 | C3 | semidirect |
| 9. C31×#6897 | C3 | semidirect |
| 13. #14578887 | C32 | semidirect |
| 14. #14578886 | C32 | semidirect |
| 15. (C31⋊C9)⋊C9 | C32 | semidirect |
| 16. (C31⋊C9)⋊C9 | C32 | semidirect |
| 17. (C31⋊C9)⋊C9 | C32 | semidirect |
| 23. C9×C31⋊C9 | C32 | semidirect |
| 24. C31×C9⋊C9 | C32 | semidirect |
| 26. C92×C31 | C32 | semidirect |
| 56. #6897 | C31⋊C3 | direct (N × H) |
| 64. C31⋊C3 | #6897 | direct (N × H) |
| 73. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 81. C92 | C3×C31⋊C3 | semidirect |
| 82. C31 | C3×#6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419347 | 3 |
| #21419346 | 3 |
| #21419345 | 3 |
| #21419344 | 3 |
| #21419343 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C92×C31⋊C3 | 3 |
| C31×#6897 | 3 |
| C3×#6897 | 31 |