Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
644 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 1. #22582592 | C3 | semidirect |
| 2. #22582591 | C3 | semidirect |
| 3. #22582582 | C3 | semidirect |
| 4. #22582581 | C3 | semidirect |
| 5. #22582578 | C3 | semidirect |
| 6. #22582577 | C3 | semidirect |
| 7. #22582576 | C3 | semidirect |
| 8. #22582575 | C3 | semidirect |
| 11. #22582536 | C3 | semidirect |
| 12. #22582535 | C3 | semidirect |
| 15. C37×#6887 | C3 | semidirect |
| 21. #15688506 | C32 | semidirect |
| 22. #15688505 | C32 | semidirect |
| 23. #15688504 | C32 | semidirect |
| 24. #15688504 | C32 | semidirect |
| 25. #15688504 | C32 | semidirect |
| 26. #15688504 | C32 | semidirect |
| 27. #15688504 | C32 | semidirect |
| 28. #15688504 | C32 | semidirect |
| 29. #15688504 | C32 | semidirect |
| 30. #15688504 | C32 | semidirect |
| 46. C9×#66524 | C32 | semidirect |
| 48. C37×C9⋊C9 | C32 | semidirect |
| 52. C92×C37 | C32 | semidirect |
| 119. #6887 | C37⋊C3 | semidirect |
| 146. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 166. C92 | C3×C37⋊C3 | semidirect |
| 167. C37 | #10624902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582592 | 3 |
| #22582591 | 3 |
| #22582582 | 3 |
| #22582581 | 3 |
| #22582578 | 3 |
| #22582577 | 3 |
| #22582576 | 3 |
| #22582575 | 3 |
| #22582553 | 3 |
| #22582552 | 3 |
| #22582536 | 3 |
| #22582535 | 3 |
| C3×#15688502 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×#6887 | 3 |
| #10624902 | 37 |