Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
824 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 292 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. #22582576 | C3 | semidirect |
| 3. #22582575 | C3 | semidirect |
| 4. #22582574 | C3 | semidirect |
| 5. #22582573 | C3 | semidirect |
| 6. #22582568 | C3 | semidirect |
| 8. #22582548 | C3 | semidirect |
| 9. 3−1+2×#66524 | C3 | semidirect |
| 10. #22582535 | C3 | semidirect |
| 22. #15688506 | C32 | semidirect |
| 23. #15688505 | C32 | semidirect |
| 24. #15688504 | C32 | semidirect |
| 25. #15688504 | C32 | semidirect |
| 26. #15688504 | C32 | semidirect |
| 30. C9×#66524 | C32 | semidirect |
| 51. C3×#66524 | 3−1+2 | semidirect |
| 120. C37 | #10624872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| #22582576 | 3 |
| #22582575 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582568 | 3 |
| #22582554 | 3 |
| #22582548 | 3 |
| 3−1+2×#66524 | 3 |
| #22582535 | 3 |
| C37×#6891 | 3 |
| #10624872 | 37 |