Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 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. #21419306 | C3 | semidirect |
| 4. C9×#11719689 | C3 | semidirect |
| 7. #21419293 | C3 | semidirect |
| 8. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 10. #14578911 | C9 | semidirect |
| 32. #11719689 | C3×C9 | semidirect |
| 35. C3×C31⋊C9 | C3×C9 | semidirect |
| 87. C31 | #10624864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578911 | 3 |
| #21419306 | 3 |
| C9×#11719689 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419293 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624864 | 31 |