Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
434 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 10. C32×#4296 | C9 | semidirect |
| 13. C32⋊#4296 | C9 | semidirect |
| 16. C32⋊#4294 | C9 | semidirect |
| 18. C19×C32⋊C9 | C9 | semidirect |
| 108. C32⋊C9 | #4296 | semidirect |
| 154. C19 | #10624466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| C3×C32⋊#4296 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| #10624466 | 19 |