Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
716 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 274 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. #22582601 | C3 | semidirect |
| 3. #22582601 | C3 | semidirect |
| 4. #22582600 | C3 | semidirect |
| 5. #22582599 | C3 | semidirect |
| 6. #22582598 | C3 | semidirect |
| 7. #22582597 | C3 | semidirect |
| 8. #22582596 | C3 | semidirect |
| 9. #22582595 | C3 | semidirect |
| 10. #22582577 | C3 | semidirect |
| 12. #22582537 | C3 | semidirect |
| 13. #22582536 | C3 | semidirect |
| 14. C37×#6900 | C3 | semidirect |
| 25. #15688506 | C32 | semidirect |
| 26. #15688506 | C32 | semidirect |
| 27. #15688505 | C32 | semidirect |
| 28. #15688505 | C32 | semidirect |
| 29. #15688504 | C32 | semidirect |
| 30. #15688504 | C32 | semidirect |
| 31. #15688504 | C32 | semidirect |
| 32. #15688504 | C32 | semidirect |
| 33. #15688504 | C32 | semidirect |
| 34. #15688504 | C32 | semidirect |
| 35. #15688504 | C32 | semidirect |
| 42. C9×#66524 | C32 | semidirect |
| 43. C9×#66524 | C32 | semidirect |
| 46. C37×C9⋊C9 | C32 | semidirect |
| 47. C37×C9⋊C9 | C32 | semidirect |
| 48. C92×C37 | C32 | semidirect |
| 74. C9×C37⋊C3 | 3−1+2 | semidirect |
| 99. #6900 | C37⋊C3 | semidirect |
| 139. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 140. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 149. C92 | C3×C37⋊C3 | semidirect |
| 150. C37 | #10624884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| #22582601 | 3 |
| #22582600 | 3 |
| #22582599 | 3 |
| #22582598 | 3 |
| #22582597 | 3 |
| #22582596 | 3 |
| #22582595 | 3 |
| #22582577 | 3 |
| #22582551 | 3 |
| #22582537 | 3 |
| #22582536 | 3 |
| C37×#6900 | 3 |
| #10624884 | 37 |