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 |
|---|---|---|
| 1. #22582594 | C3 | direct (N × H) |
| 2. C3×#15688506 | C3 | semidirect |
| 3. C3×#15688505 | C3 | semidirect |
| 4. C3×#15688504 | C3 | semidirect |
| 6. C3×C9×#66524 | C3 | semidirect |
| 11. #15688506 | C32 | semidirect |
| 12. #15688505 | C32 | semidirect |
| 13. #15688504 | C32 | semidirect |
| 15. C9×#66524 | C32 | semidirect |
| 56. C3×C37 | #6899 | semidirect |
| 72. C37 | C3×#6899 | semidirect |
| 100. C3 | #22582594 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582594 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×C9×#66524 | 3 |
| C32×3−1+2×C37 | 3 |
| C3×#6899 | 37 |