Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
788 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 328 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. #22582600 | C3 | direct (N × H) |
| 3. C3×#15688506 | C3 | semidirect |
| 4. C3×#15688505 | C3 | semidirect |
| 5. C3×#15688504 | C3 | semidirect |
| 7. C3×C9×#66524 | C3 | semidirect |
| 8. C3×C37×C9⋊C9 | C3 | semidirect |
| 16. #15688506 | C32 | semidirect |
| 17. #15688505 | C32 | semidirect |
| 18. #15688504 | C32 | semidirect |
| 20. C9×#66524 | C32 | semidirect |
| 23. C37×C9⋊C9 | C32 | semidirect |
| 59. C3×C9⋊C9 | C37⋊C3 | semidirect |
| 62. C3×C37 | #6899 | semidirect |
| 78. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 81. C37 | C3×#6899 | semidirect |
| 112. C3 | #22582600 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758606 | 3 |
| #22582600 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C3×#15688502 | 3 |
| C3×C9×#66524 | 3 |
| C3×C37×C9⋊C9 | 3 |
| C3×#6899 | 37 |