Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
836 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 316 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. #22582601 | C3 | semidirect |
| 3. #22582580 | C3 | semidirect |
| 4. #22582572 | C3 | semidirect |
| 5. #22582571 | C3 | semidirect |
| 6. #22582568 | C3 | semidirect |
| 8. 3−1+2×#66524 | C3 | semidirect |
| 9. C9×#11758608 | C3 | semidirect |
| 19. #15688506 | C32 | semidirect |
| 20. #15688505 | C32 | semidirect |
| 21. #15688504 | C32 | semidirect |
| 22. #15688504 | C32 | semidirect |
| 23. #15688504 | C32 | semidirect |
| 27. C9×#66524 | C32 | semidirect |
| 45. 3−1+2×C37 | 3−1+2 | semidirect |
| 54. #11758608 | 3−1+2 | direct (N × H) |
| 76. C9×C37 | C3×3−1+2 | semidirect |
| 80. #66524 | C3×3−1+2 | semidirect |
| 122. C37 | 3−1+22 | semidirect |
| 139. 3−1+2 | #11758608 | direct (N × H) |
| 167. C9 | C3×#11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| #22582601 | 3 |
| #22582580 | 3 |
| #22582572 | 3 |
| #22582571 | 3 |
| #22582568 | 3 |
| #22582554 | 3 |
| 3−1+2×#66524 | 3 |
| C9×#11758608 | 3 |
| C32×3−1+2×C37 | 3 |
| 3−1+22 | 37 |