Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
620 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582585 | C3 | semidirect |
| 2. #22582580 | C3 | semidirect |
| 3. #22582574 | C3 | semidirect |
| 4. #22582573 | C3 | semidirect |
| 7. #22582548 | C3 | semidirect |
| 15. #15688506 | C32 | semidirect |
| 16. #15688505 | C32 | semidirect |
| 17. #15688504 | C32 | semidirect |
| 18. #15688504 | C32 | semidirect |
| 19. #15688504 | C32 | semidirect |
| 26. C9×#66524 | C32 | semidirect |
| 108. C37 | #10624889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582585 | 3 |
| #22582580 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582554 | 3 |
| #22582548 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×#6891 | 3 |
| #10624889 | 37 |