Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
836 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 310 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. #21419335 | C3 | direct (N × H) |
| 3. C3×#14578887 | C3 | semidirect |
| 4. C3×#14578886 | 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 |
| 10. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 14. C3×C31×C9⋊C9 | C3 | semidirect |
| 26. #14578887 | C32 | semidirect |
| 27. #14578886 | 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 |
| 32. (C31⋊C9)⋊C9 | C32 | semidirect |
| 33. (C31⋊C9)⋊C9 | C32 | semidirect |
| 41. C31×C9⋊C9 | C32 | semidirect |
| 106. C3×C9⋊C9 | C31⋊C3 | semidirect |
| 110. C3×C31 | #6895 | semidirect |
| 139. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 143. C31 | C3×#6895 | semidirect |
| 198. C3 | #21419335 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| #21419335 | 3 |
| C3×#14578887 | 3 |
| C3×#14578886 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C31×C9⋊C9 | 3 |
| C3×#6895 | 31 |