Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
824 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 283 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. #22582578 | C3 | semidirect |
| 3. #22582576 | C3 | semidirect |
| 4. #22582569 | C3 | semidirect |
| 6. #22582542 | C3 | semidirect |
| 7. #22582535 | C3 | semidirect |
| 8. C37×#6895 | C3 | semidirect |
| 16. #15688505 | C32 | semidirect |
| 17. #15688504 | C32 | semidirect |
| 18. #15688504 | C32 | semidirect |
| 19. #15688504 | C32 | semidirect |
| 22. C9×#66524 | C32 | semidirect |
| 24. C37×C9⋊C9 | C32 | semidirect |
| 34. C3×#66524 | 3−1+2 | semidirect |
| 59. #6895 | C37⋊C3 | semidirect |
| 80. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 85. C37 | #10624872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| #22582578 | 3 |
| #22582576 | 3 |
| #22582569 | 3 |
| #22582552 | 3 |
| #22582542 | 3 |
| #22582535 | 3 |
| C37×#6895 | 3 |
| #10624872 | 37 |