Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
608 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 117 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. (C3×#4296)⋊C9 | C3 | semidirect |
| 11. C3×#10587025 | C9 | semidirect |
| 12. C3×#10587022 | C9 | semidirect |
| 13. C3×#10587023 | C9 | semidirect |
| 17. C3×C19×3−1+2 | C9 | semidirect |
| 32. C3×#4296 | 3−1+2 | semidirect |
| 34. C3×C9×C19 | C3×C9 | semidirect |
| 36. C3×#4294 | C3×C9 | semidirect |
| 69. C3×3−1+2 | #4296 | semidirect |
| 105. C3×C9 | C3×#4296 | semidirect |
| 106. C19 | #10624558 | 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 |
| (C3×#4296)⋊C9 | 3 |
| C3×3−1+2×C19⋊C3 | 3 |
| #10624558 | 19 |