Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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×C9×C31⋊C9 | C3 | semidirect |
| 5. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 6. #21419236 | C3 | semidirect |
| 8. #21419227 | C3 | semidirect |
| 9. C9×3−1+2×C31 | C3 | semidirect |
| 15. #14578898 | C9 | direct (N × H) |
| 31. 3−1+2×C31 | C3×C9 | semidirect |
| 40. #11719689 | C3×C9 | semidirect |
| 48. C3×C31⋊C9 | C3×C9 | semidirect |
| 62. C9×C31 | #731 | semidirect |
| 70. C9×3−1+2 | C31⋊C3 | semidirect |
| 101. C31 | C9×#731 | semidirect |
| 107. 3−1+2 | C9×C31⋊C3 | semidirect |
| 140. C9 | #14578898 | direct (N × H) |
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×C9×C31⋊C9 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419236 | 3 |
| #21419233 | 3 |
| #21419227 | 3 |
| C9×3−1+2×C31 | 3 |
| C9×#731 | 31 |