Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
482 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 11. #15688538 | C9 | semidirect |
| 12. #15688537 | C9 | semidirect |
| 14. C9×#66526 | C9 | semidirect |
| 17. #15688506 | C9 | semidirect |
| 18. #15688505 | C9 | semidirect |
| 19. #15688504 | C9 | semidirect |
| 20. C37×C9⋊C9 | C9 | semidirect |
| 52. #66526 | C9⋊C9 | direct (N × H) |
| 54. C9×C37 | C92 | semidirect |
| 57. #66524 | C92 | semidirect |
| 81. C9⋊C9 | #66526 | direct (N × H) |
| 84. C37 | C9×C9⋊C9 | semidirect |
| 120. C9 | C9×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688538 | 3 |
| C3×#15688537 | 3 |
| C3×C9×#66526 | 3 |
| (C3×#66526)⋊C9 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C9×C9⋊C9 | 37 |