Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 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. #21419297 | C3 | semidirect |
| 3. C3×C9×C31⋊C9 | C3 | semidirect |
| 4. #21419233 | C3 | semidirect |
| 5. #21419230 | C3 | semidirect |
| 6. C31×#6868 | C3 | semidirect |
| 11. #14578900 | C9 | semidirect |
| 23. C3×C9×C31 | C3×C9 | semidirect |
| 25. C32⋊(C31⋊C3) | C3×C9 | semidirect |
| 47. C31⋊C9 | #732 | semidirect |
| 53. #6868 | C31⋊C3 | semidirect |
| 71. C31 | C9×#732 | semidirect |
| 86. 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 |
|---|---|
| C3×#14578900 | 3 |
| #21419297 | 3 |
| C3×C9×C31⋊C9 | 3 |
| #21419233 | 3 |
| #21419230 | 3 |
| C31×#6868 | 3 |
| C9×#732 | 31 |