Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
622 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 262 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. #22582574 | C3 | semidirect |
| 7. #22582572 | C3 | semidirect |
| 8. #22582572 | C3 | semidirect |
| 11. #22582548 | C3 | semidirect |
| 12. #22582538 | C3 | semidirect |
| 13. #22582535 | C3 | semidirect |
| 14. C3×#15688506 | C3 | semidirect |
| 151. C37 | #10624904 | 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 |
| #22582574 | 3 |
| #22582572 | 3 |
| #22582562 | 3 |
| #22582556 | 3 |
| #22582548 | 3 |
| #22582538 | 3 |
| #22582535 | 3 |
| C3×#15688506 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624904 | 37 |