Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
236 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22582575 | C3 | semidirect |
| 2. #22582561 | C3 | semidirect |
| 3. #22582539 | C3 | semidirect |
| 4. #22582539 | C3 | semidirect |
| 5. #22582458 | C3 | semidirect |
| 6. #22582458 | C3 | semidirect |
| 7. #22582453 | C3 | semidirect |
| 8. #22582453 | C3 | semidirect |
| 9. #22582452 | C3 | semidirect |
| 10. #22582443 | C3 | semidirect |
| 11. #22582443 | C3 | semidirect |
| 12. #22582443 | C3 | semidirect |
| 13. C37×#6861 | C3 | semidirect |
| 98. #6861 | C37⋊C3 | semidirect |
| 138. C37 | #10624622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582575 | 3 |
| #22582561 | 3 |
| #22582539 | 3 |
| #22582458 | 3 |
| #22582453 | 3 |
| #22582452 | 3 |
| #22582443 | 3 |
| C37×#6861 | 3 |
| #10624622 | 37 |