Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 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. #22582573 | C3 | semidirect |
| 2. #22582562 | C3 | semidirect |
| 3. #22582548 | C3 | semidirect |
| 4. #22582539 | C3 | semidirect |
| 5. #22582455 | C3 | semidirect |
| 6. #22582455 | C3 | semidirect |
| 7. #22582450 | C3 | semidirect |
| 8. #22582450 | C3 | semidirect |
| 9. #22582446 | C3 | semidirect |
| 10. #22582446 | C3 | semidirect |
| 11. #22582445 | C3 | semidirect |
| 13. C37×#6859 | C3 | semidirect |
| 96. #6859 | C37⋊C3 | semidirect |
| 135. C37 | #10624623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582573 | 3 |
| #22582562 | 3 |
| #22582548 | 3 |
| #22582539 | 3 |
| #22582455 | 3 |
| #22582450 | 3 |
| #22582446 | 3 |
| #22582445 | 3 |
| #22582442 | 3 |
| C37×#6859 | 3 |
| #10624623 | 37 |