Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
718 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 2. #22582602 | C3 | semidirect |
| 3. #22582599 | C3 | semidirect |
| 4. #22582583 | C3 | semidirect |
| 5. #22582581 | C3 | semidirect |
| 6. #22582576 | C3 | semidirect |
| 7. #22582574 | C3 | semidirect |
| 8. #22582571 | C3 | semidirect |
| 9. #22582567 | C3 | semidirect |
| 12. 3−1+2×#66524 | C3 | semidirect |
| 13. C9×#11758605 | C3 | semidirect |
| 14. C3×#15688505 | C3 | semidirect |
| 15. C9×3−1+2×C37 | C3 | semidirect |
| 55. 3−1+2×C37 | 3−1+2 | semidirect |
| 90. C9×C37 | #737 | semidirect |
| 113. C9×3−1+2 | C37⋊C3 | semidirect |
| 157. C37 | #10624901 | semidirect |
| 165. 3−1+2 | #11758605 | semidirect |
| 203. C9 | #15688532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| #22582602 | 3 |
| #22582599 | 3 |
| #22582583 | 3 |
| #22582581 | 3 |
| #22582576 | 3 |
| #22582574 | 3 |
| #22582571 | 3 |
| #22582567 | 3 |
| #22582561 | 3 |
| #22582558 | 3 |
| 3−1+2×#66524 | 3 |
| C9×#11758605 | 3 |
| C3×#15688505 | 3 |
| C9×3−1+2×C37 | 3 |
| #10624901 | 37 |