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 |
|---|---|---|
| 1. #21419352 | C3 | direct (N × H) |
| 2. C3×#14578887 | C3 | semidirect |
| 3. C3×#14578886 | C3 | semidirect |
| 4. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×C9×C31⋊C9 | C3 | semidirect |
| 11. #14578887 | C32 | semidirect |
| 12. #14578886 | C32 | semidirect |
| 13. (C31⋊C9)⋊C9 | C32 | semidirect |
| 15. C9×C31⋊C9 | C32 | semidirect |
| 56. C3×C31 | #6899 | semidirect |
| 72. C31 | C3×#6899 | semidirect |
| 100. C3 | #21419352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419352 | 3 |
| C3×#14578887 | 3 |
| C3×#14578886 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C9×C31⋊C9 | 3 |
| C32×3−1+2×C31 | 3 |
| C3×#6899 | 31 |