Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
728 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 274 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. #22582575 | C3 | semidirect |
| 5. #22582570 | C3 | semidirect |
| 6. #22582567 | C3 | semidirect |
| 8. C37×#6895 | C3 | semidirect |
| 16. #15688506 | C32 | semidirect |
| 17. #15688505 | C32 | semidirect |
| 18. #15688504 | C32 | semidirect |
| 19. #15688504 | C32 | semidirect |
| 20. #15688504 | C32 | semidirect |
| 24. C37×C9⋊C9 | C32 | semidirect |
| 60. #6895 | C37⋊C3 | semidirect |
| 81. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 85. C37 | #10624886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758605 | 3 |
| #22582578 | 3 |
| #22582576 | 3 |
| #22582575 | 3 |
| #22582570 | 3 |
| #22582567 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C37×#6895 | 3 |
| #10624886 | 37 |