Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
662 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 268 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. #22582593 | C3 | semidirect |
| 2. #22582590 | C3 | semidirect |
| 3. #22582585 | C3 | semidirect |
| 4. #22582579 | C3 | semidirect |
| 5. #22582576 | C3 | semidirect |
| 6. #22582575 | C3 | semidirect |
| 7. #22582574 | C3 | semidirect |
| 8. #22582573 | C3 | semidirect |
| 11. C9×#11758608 | C3 | semidirect |
| 12. C9×#11758608 | C3 | semidirect |
| 13. #22582538 | C3 | semidirect |
| 14. C3×C9×#66524 | C3 | semidirect |
| 151. C37 | #10624877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582593 | 3 |
| #22582590 | 3 |
| #22582585 | 3 |
| #22582579 | 3 |
| #22582576 | 3 |
| #22582575 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582562 | 3 |
| #22582556 | 3 |
| C9×#11758608 | 3 |
| #22582538 | 3 |
| C3×C9×#66524 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624877 | 37 |