Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
692 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|---|
| 1. #21419343 | C3 | direct (N × H) |
| 2. C3×#14578887 | C3 | semidirect |
| 3. C3×#14578886 | C3 | semidirect |
| 4. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 5. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 7. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 8. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 9. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 13. C3×C9×C31⋊C9 | C3 | semidirect |
| 24. #14578887 | C32 | semidirect |
| 25. #14578886 | C32 | semidirect |
| 26. (C31⋊C9)⋊C9 | C32 | semidirect |
| 27. (C31⋊C9)⋊C9 | C32 | semidirect |
| 28. (C31⋊C9)⋊C9 | C32 | semidirect |
| 29. (C31⋊C9)⋊C9 | C32 | semidirect |
| 30. (C31⋊C9)⋊C9 | C32 | semidirect |
| 31. (C31⋊C9)⋊C9 | C32 | semidirect |
| 35. C9×C31⋊C9 | C32 | semidirect |
| 109. C3×C31 | #6897 | semidirect |
| 140. C31 | C3×#6897 | semidirect |
| 194. C3 | #21419343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419343 | 3 |
| C3×#14578887 | 3 |
| C3×#14578886 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×#6897 | 31 |