Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22582548 | C3 | semidirect |
| 3. #22582539 | C3 | semidirect |
| 4. C3×C32⋊#66524 | C3 | semidirect |
| 5. #22582481 | C3 | semidirect |
| 6. #22582478 | C3 | semidirect |
| 7. #22582475 | C3 | semidirect |
| 8. #22582468 | C3 | semidirect |
| 9. C37×#6866 | C3 | semidirect |
| 15. #15688513 | C9 | semidirect |
| 31. C33×C37 | C3×C9 | semidirect |
| 39. #11758608 | C3×C9 | semidirect |
| 79. #6866 | C37⋊C3 | semidirect |
| 104. C37 | AΣL(1,𝔽27)⋊C9 | semidirect |
| 110. C33 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688513 | 3 |
| #22582548 | 3 |
| #22582539 | 3 |
| C3×C32⋊#66524 | 3 |
| #22582481 | 3 |
| #22582478 | 3 |
| #22582475 | 3 |
| #22582468 | 3 |
| C37×#6866 | 3 |
| AΣL(1,𝔽27)⋊C9 | 37 |