Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
836 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. #22582604 | C3 | semidirect |
| 4. #22582604 | C3 | semidirect |
| 5. #22582583 | C3 | semidirect |
| 6. #22582582 | C3 | semidirect |
| 7. #22582574 | C3 | semidirect |
| 8. #22582571 | C3 | semidirect |
| 9. #22582569 | C3 | semidirect |
| 10. #22582568 | C3 | semidirect |
| 12. #22582548 | C3 | semidirect |
| 13. C9×#11758608 | C3 | semidirect |
| 14. #22582542 | C3 | semidirect |
| 15. C37×#6894 | C3 | semidirect |
| 32. #15688505 | C32 | semidirect |
| 33. #15688505 | C32 | semidirect |
| 34. #15688504 | C32 | semidirect |
| 35. #15688504 | C32 | semidirect |
| 36. #15688504 | C32 | semidirect |
| 37. #15688504 | C32 | semidirect |
| 38. #15688504 | C32 | semidirect |
| 39. #15688504 | C32 | semidirect |
| 40. #15688504 | C32 | semidirect |
| 41. #15688504 | C32 | semidirect |
| 42. #15688504 | C32 | semidirect |
| 47. C9×#66524 | C32 | semidirect |
| 48. C9×#66524 | C32 | semidirect |
| 51. C37×C9⋊C9 | C32 | semidirect |
| 52. C37×C9⋊C9 | C32 | semidirect |
| 68. #11758608 | 3−1+2 | semidirect |
| 84. #11758606 | 3−1+2 | semidirect |
| 105. C9×C37 | C3×3−1+2 | semidirect |
| 111. #66524 | C3×3−1+2 | semidirect |
| 112. #66524 | C3×3−1+2 | semidirect |
| 123. #6894 | C37⋊C3 | semidirect |
| 164. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 165. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 173. C37 | 3−1+22 | semidirect |
| 231. C9 | 3−1+2×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758606 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| #22582604 | 3 |
| #22582583 | 3 |
| #22582582 | 3 |
| #22582574 | 3 |
| #22582571 | 3 |
| #22582569 | 3 |
| #22582568 | 3 |
| #22582552 | 3 |
| #22582548 | 3 |
| C9×#11758608 | 3 |
| #22582542 | 3 |
| C37×#6894 | 3 |
| 3−1+22 | 37 |