Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
788 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 328 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. #21419358 | C3 | direct (N × H) |
| 3. C3×#14578887 | C3 | semidirect |
| 4. C3×#14578886 | C3 | semidirect |
| 5. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 7. C3×C9×C31⋊C9 | C3 | semidirect |
| 8. C3×C31×C9⋊C9 | C3 | semidirect |
| 16. #14578887 | C32 | semidirect |
| 17. #14578886 | C32 | semidirect |
| 18. (C31⋊C9)⋊C9 | C32 | semidirect |
| 20. C9×C31⋊C9 | C32 | semidirect |
| 23. C31×C9⋊C9 | C32 | semidirect |
| 59. C3×C9⋊C9 | C31⋊C3 | semidirect |
| 62. C3×C31 | #6899 | semidirect |
| 78. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 81. C31 | C3×#6899 | semidirect |
| 112. C3 | #21419358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719687 | 3 |
| #21419358 | 3 |
| C3×#14578887 | 3 |
| C3×#14578886 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C31×C9⋊C9 | 3 |
| C3×#6899 | 31 |