Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
190 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 190 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. #21419352 | C3 | semidirect |
| 3. #21419283 | C3 | semidirect |
| 4. #21419282 | C3 | semidirect |
| 5. #21419270 | C3 | semidirect |
| 6. #21419269 | C3 | semidirect |
| 7. #21419264 | C3 | semidirect |
| 8. #21419259 | C3 | semidirect |
| 9. C31×#6911 | C3 | semidirect |
| 11. #14578902 | C32 | semidirect |
| 12. #14578902 | C32 | semidirect |
| 13. #14578900 | C32 | semidirect |
| 16. #14578887 | C32 | semidirect |
| 17. #14578886 | C32 | semidirect |
| 20. C9×C31⋊C9 | C32 | semidirect |
| 59. #6911 | C31⋊C3 | semidirect |
| 89. C31 | #10624853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419419 | 3 |
| #21419352 | 3 |
| #21419283 | 3 |
| #21419282 | 3 |
| #21419270 | 3 |
| #21419269 | 3 |
| #21419264 | 3 |
| #21419259 | 3 |
| C31×#6911 | 3 |
| #10624853 | 31 |