Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
788 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 310 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. #22582593 | C3 | direct (N × H) |
| 3. C3×#15688506 | C3 | semidirect |
| 4. C3×#15688505 | C3 | semidirect |
| 5. C3×#15688504 | C3 | semidirect |
| 6. C3×#15688504 | C3 | semidirect |
| 7. C3×#15688504 | C3 | semidirect |
| 8. C3×#15688504 | C3 | semidirect |
| 9. C3×#15688504 | C3 | semidirect |
| 10. C3×#15688504 | C3 | semidirect |
| 13. C3×C9×#66524 | C3 | semidirect |
| 26. #15688506 | C32 | semidirect |
| 27. #15688505 | 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 |
| 36. C9×#66524 | C32 | semidirect |
| 111. C3×C37 | #6899 | semidirect |
| 143. C37 | C3×#6899 | semidirect |
| 198. C3 | #22582593 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| #22582593 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×C9×#66524 | 3 |
| C3×C37×C32⋊C9 | 3 |
| C3×#6899 | 37 |