Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
404 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #17987336 | C3 | semidirect |
| 9. C3×#10587025 | C9 | semidirect |
| 37. C3×#4294 | C3×C9 | semidirect |
| 101. C19 | #10624690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C3×C32⋊#4294 | 3 |
| #17987336 | 3 |
| C3×C19×C32⋊C9 | 3 |
| #10624690 | 19 |