Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 2. C9×#11719689 | C3 | semidirect |
| 4. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 5. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 6. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 7. #21419236 | C3 | semidirect |
| 8. #21419236 | C3 | semidirect |
| 11. #21419227 | C3 | semidirect |
| 12. #21419227 | C3 | semidirect |
| 13. C9×3−1+2×C31 | C3 | semidirect |
| 20. #14578898 | C9 | semidirect |
| 43. 3−1+2×C31 | C3×C9 | semidirect |
| 54. #11719689 | C3×C9 | semidirect |
| 66. C3×C31⋊C9 | C3×C9 | semidirect |
| 95. C9×3−1+2 | C31⋊C3 | semidirect |
| 139. C31 | #731⋊C9 | semidirect |
| 145. 3−1+2 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578898 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419236 | 3 |
| #21419233 | 3 |
| #21419227 | 3 |
| C9×3−1+2×C31 | 3 |
| #731⋊C9 | 31 |