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. #22582589 | C3 | semidirect |
| 2. #22582588 | C3 | semidirect |
| 3. #22582587 | C3 | semidirect |
| 4. #22582586 | C3 | semidirect |
| 5. #22582582 | C3 | semidirect |
| 6. #22582581 | C3 | semidirect |
| 7. #22582574 | C3 | semidirect |
| 8. #22582573 | C3 | semidirect |
| 9. #22582568 | C3 | semidirect |
| 13. C9×#11758608 | C3 | semidirect |
| 15. C9×3−1+2×C37 | C3 | semidirect |
| 21. #15688506 | C32 | semidirect |
| 22. #15688505 | C32 | semidirect |
| 23. #15688504 | C32 | semidirect |
| 24. #15688504 | C32 | semidirect |
| 25. #15688504 | C32 | semidirect |
| 26. #15688504 | C32 | semidirect |
| 27. #15688504 | C32 | semidirect |
| 28. #15688504 | C32 | semidirect |
| 29. #15688504 | C32 | semidirect |
| 30. #15688504 | C32 | semidirect |
| 31. #15688504 | C32 | semidirect |
| 47. C9×#66524 | C32 | semidirect |
| 50. C37×C9⋊C9 | C32 | semidirect |
| 53. C92×C37 | C32 | semidirect |
| 122. C9×3−1+2 | C37⋊C3 | semidirect |
| 150. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 169. C92 | C3×C37⋊C3 | semidirect |
| 170. C37 | #10624889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582589 | 3 |
| #22582588 | 3 |
| #22582587 | 3 |
| #22582586 | 3 |
| #22582582 | 3 |
| #22582581 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582568 | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| #22582551 | 3 |
| C9×#11758608 | 3 |
| C3×#15688502 | 3 |
| C9×3−1+2×C37 | 3 |
| #10624889 | 37 |