Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
404 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 94 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. #17987339 | C3 | semidirect |
| 4. #17987338 | C3 | semidirect |
| 5. C19×#6868 | C3 | semidirect |
| 9. C3×#10587023 | C9 | semidirect |
| 26. C3×C9×C19 | C3×C9 | semidirect |
| 30. C3×#4294 | C3×C9 | semidirect |
| 37. #6868 | C19⋊C3 | semidirect |
| 83. C3×C9 | C9×C19⋊C3 | semidirect |
| 84. C19 | #10624691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587023 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| #17987339 | 3 |
| #17987338 | 3 |
| C19×#6868 | 3 |
| #10624691 | 19 |