Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
788 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 788 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. #22582600 | C3 | semidirect |
| 3. #22582599 | C3 | semidirect |
| 4. #22582598 | C3 | semidirect |
| 5. #22582597 | C3 | semidirect |
| 6. #22582596 | C3 | semidirect |
| 7. #22582595 | C3 | semidirect |
| 8. #22582594 | C3 | semidirect |
| 9. #22582593 | C3 | semidirect |
| 10. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 11. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 13. C92×C37⋊C3 | C3 | semidirect |
| 14. C37×#6899 | C3 | semidirect |
| 26. #15688506 | C32 | semidirect |
| 27. #15688506 | C32 | semidirect |
| 28. #15688505 | C32 | semidirect |
| 29. #15688505 | 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 |
| 41. C9×#66524 | C32 | semidirect |
| 42. C9×#66524 | C32 | semidirect |
| 44. C37×C9⋊C9 | C32 | semidirect |
| 45. C37×C9⋊C9 | C32 | semidirect |
| 47. C92×C37 | C32 | semidirect |
| 104. #6899 | C37⋊C3 | direct (N × H) |
| 114. C37⋊C3 | #6899 | direct (N × H) |
| 137. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 138. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 147. C92 | C3×C37⋊C3 | semidirect |
| 148. C37 | C3×#6899 | 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 |
| #22582600 | 3 |
| #22582599 | 3 |
| #22582598 | 3 |
| #22582597 | 3 |
| #22582596 | 3 |
| #22582595 | 3 |
| #22582594 | 3 |
| #22582593 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C92×C37⋊C3 | 3 |
| C37×#6899 | 3 |
| C3×#6899 | 37 |