Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 30. #15688506 | C9 | semidirect |
| 31. #15688505 | C9 | semidirect |
| 32. #15688504 | C9 | semidirect |
| 33. #15688504 | C9 | semidirect |
| 34. #15688504 | C9 | semidirect |
| 35. #15688504 | C9 | semidirect |
| 36. #15688504 | C9 | semidirect |
| 37. #15688504 | C9 | semidirect |
| 38. C37×C9⋊C9 | C9 | semidirect |
| 184. C9⋊C9 | #66526 | semidirect |
| 186. C37 | #10624559 | 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 |
| #10624559 | 37 |