Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
824 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 824 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 |
|---|---|---|
| 1. #22582578 | C3 | semidirect |
| 2. #22582572 | C3 | semidirect |
| 3. #22582571 | C3 | semidirect |
| 5. C9×#11758608 | C3 | semidirect |
| 6. #22582538 | C3 | semidirect |
| 9. #15688506 | C32 | semidirect |
| 10. #15688505 | C32 | semidirect |
| 11. #15688504 | C32 | semidirect |
| 14. C9×#66524 | C32 | semidirect |
| 30. C3×C9×C37 | 3−1+2 | semidirect |
| 75. C37 | #10624872 | semidirect |
| 86. C3×C9 | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582578 | 3 |
| #22582572 | 3 |
| #22582571 | 3 |
| #22582554 | 3 |
| C9×#11758608 | 3 |
| #22582538 | 3 |
| C33×C9×C37 | 3 |
| #10624872 | 37 |