Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
944 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 454 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. #21419306 | C3 | semidirect |
| 3. C9×#11719689 | C3 | semidirect |
| 4. #21419293 | C3 | semidirect |
| 7. C3×#11719689 | C9 | semidirect |
| 12. (C31⋊C9)⋊C9 | C32 | semidirect |
| 16. C9×C31⋊C9 | C32 | semidirect |
| 29. #11719689 | C3×C9 | semidirect |
| 30. #11719689 | C3×C9 | semidirect |
| 32. C3×C31⋊C9 | C3×C9 | semidirect |
| 77. C31 | #10624863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| #21419306 | 3 |
| C9×#11719689 | 3 |
| #21419293 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C31×C32⋊C9 | 3 |
| #10624863 | 31 |