Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
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. #13095307 | C9 | semidirect |
| 31. #13095306 | C9 | semidirect |
| 32. #13095305 | C9 | semidirect |
| 33. #13095305 | C9 | semidirect |
| 34. #13095305 | C9 | semidirect |
| 35. #13095305 | C9 | semidirect |
| 36. #13095305 | C9 | semidirect |
| 37. #13095305 | C9 | semidirect |
| 38. C19×C9⋊C9 | C9 | semidirect |
| 171. C9⋊C9 | #4296 | semidirect |
| 247. C19 | #10624559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095339 | 3 |
| C3×#13095338 | 3 |
| C3×C9×#4296 | 3 |
| (C3×#4296)⋊C9 | 3 |
| C19⋊C3×C9⋊C9 | 3 |
| #10624559 | 19 |