Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
596 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 250 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. #22582600 | C3 | semidirect |
| 2. #22582598 | C3 | semidirect |
| 3. #22582598 | C3 | semidirect |
| 4. #22582598 | C3 | semidirect |
| 5. #22582595 | C3 | semidirect |
| 6. #22582588 | C3 | semidirect |
| 7. #22582588 | C3 | semidirect |
| 8. #22582587 | C3 | semidirect |
| 9. #22582580 | C3 | semidirect |
| 10. #22582579 | C3 | semidirect |
| 13. C37×#6896 | C3 | semidirect |
| 18. #15688506 | C32 | semidirect |
| 19. #15688506 | C32 | semidirect |
| 20. #15688505 | C32 | semidirect |
| 21. #15688505 | C32 | semidirect |
| 22. #15688504 | 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 |
| 32. #15688504 | C32 | semidirect |
| 33. #15688504 | C32 | semidirect |
| 45. C9×#66524 | C32 | semidirect |
| 46. C9×#66524 | C32 | semidirect |
| 48. C37×C9⋊C9 | C32 | semidirect |
| 49. C37×C9⋊C9 | C32 | semidirect |
| 51. C92×C37 | C32 | semidirect |
| 101. #6896 | C37⋊C3 | semidirect |
| 130. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 131. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 146. C92 | C3×C37⋊C3 | semidirect |
| 147. C37 | #10624911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582600 | 3 |
| #22582598 | 3 |
| #22582595 | 3 |
| #22582588 | 3 |
| #22582587 | 3 |
| #22582580 | 3 |
| #22582579 | 3 |
| #22582552 | 3 |
| #22582551 | 3 |
| C37×#6896 | 3 |
| #10624911 | 37 |