Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
692 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 271 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. #22582589 | C3 | semidirect |
| 2. #22582588 | C3 | semidirect |
| 3. #22582587 | C3 | semidirect |
| 4. #22582586 | C3 | semidirect |
| 5. #22582585 | C3 | semidirect |
| 6. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 8. C92×C37⋊C3 | C3 | semidirect |
| 9. C37×#6897 | C3 | semidirect |
| 13. #15688506 | C32 | semidirect |
| 14. #15688505 | C32 | semidirect |
| 15. #15688504 | C32 | semidirect |
| 16. #15688504 | C32 | semidirect |
| 17. #15688504 | C32 | semidirect |
| 23. C9×#66524 | C32 | semidirect |
| 24. C37×C9⋊C9 | C32 | semidirect |
| 26. C92×C37 | C32 | semidirect |
| 56. #6897 | C37⋊C3 | direct (N × H) |
| 64. C37⋊C3 | #6897 | direct (N × H) |
| 73. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 81. C92 | C3×C37⋊C3 | semidirect |
| 82. C37 | C3×#6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582589 | 3 |
| #22582588 | 3 |
| #22582587 | 3 |
| #22582586 | 3 |
| #22582585 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C92×C37⋊C3 | 3 |
| C37×#6897 | 3 |
| C3×#6897 | 37 |