Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22582548 | C3 | semidirect |
| 4. C3×C9×#66524 | C3 | semidirect |
| 5. #22582481 | C3 | semidirect |
| 6. #22582478 | C3 | semidirect |
| 8. #22582470 | C3 | semidirect |
| 9. C37×#6867 | C3 | semidirect |
| 15. #15688516 | C9 | semidirect |
| 32. C3×C9×C37 | C3×C9 | semidirect |
| 36. #11758608 | C3×C9 | semidirect |
| 63. #66524 | #731 | semidirect |
| 72. #6867 | C37⋊C3 | semidirect |
| 95. C37 | C9×#731 | semidirect |
| 115. C3×C9 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688516 | 3 |
| #22582548 | 3 |
| #22582539 | 3 |
| C3×C9×#66524 | 3 |
| #22582481 | 3 |
| #22582478 | 3 |
| #22582475 | 3 |
| #22582470 | 3 |
| C37×#6867 | 3 |
| C9×#731 | 37 |