Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
482 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 11. #15688504 | C9 | direct (N × H) |
| 14. C9×#66524 | C9 | semidirect |
| 44. C9×C37 | C9⋊C9 | semidirect |
| 48. #66524 | C92 | semidirect |
| 72. C37 | C9×C9⋊C9 | semidirect |
| 102. C9 | #15688504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688504 | 3 |
| C3×C9×#66524 | 3 |
| #22582441 | 3 |
| C3×C92×C37 | 3 |
| C9×C9⋊C9 | 37 |