Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 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. #22582578 | C3 | semidirect |
| 2. #22582538 | C3 | semidirect |
| 4. #22582471 | C3 | semidirect |
| 5. #22582471 | C3 | semidirect |
| 6. #22582471 | C3 | semidirect |
| 7. #22582469 | C3 | semidirect |
| 8. #22582469 | C3 | semidirect |
| 9. #22582469 | C3 | semidirect |
| 13. C37×#6895 | C3 | semidirect |
| 88. #6895 | C37⋊C3 | semidirect |
| 131. C37 | #10624810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582578 | 3 |
| #22582538 | 3 |
| C3×#15688502 | 3 |
| #22582471 | 3 |
| #22582469 | 3 |
| #22582467 | 3 |
| C37×#6895 | 3 |
| #10624810 | 37 |