Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
230 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 102 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. #17987573 | C3 | semidirect |
| 2. #17987572 | C3 | semidirect |
| 4. C9×#10587020 | C3 | semidirect |
| 28. C3×#4294 | C27 | semidirect |
| 98. C19 | #10624710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987573 | 3 |
| #17987572 | 3 |
| C32⋊#10587020 | 3 |
| C9×#10587020 | 3 |
| C3×C9×#4294 | 3 |
| #10624710 | 19 |