Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
986 conjugacy classes of subgroups; only the 472 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 472 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 |
|---|---|---|
| 2. C9×#10587023 | C3 | semidirect |
| 3. C9×#10587022 | C3 | semidirect |
| 4. C9×#10587025 | C3 | semidirect |
| 6. #17987405 | C3 | semidirect |
| 7. #17987403 | C3 | semidirect |
| 8. C92×C19⋊C3 | C3 | semidirect |
| 9. C3×C92×C19 | C3 | semidirect |
| 10. #13095332 | C9 | direct (N × H) |
| 34. C3×C9×C19 | C3×C9 | semidirect |
| 41. #10587025 | C3×C9 | semidirect |
| 44. #10587023 | C3×C9 | semidirect |
| 45. #10587022 | C3×C9 | semidirect |
| 47. C9×C19⋊C3 | C3×C9 | semidirect |
| 56. C3×C92 | C19⋊C3 | semidirect |
| 66. C9×C19 | #737 | semidirect |
| 104. C3×C9 | C9×C19⋊C3 | semidirect |
| 110. C19 | C9×#737 | semidirect |
| 122. C9 | #13095332 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| C9×#10587023 | 3 |
| C9×#10587022 | 3 |
| C9×#10587025 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| #17987405 | 3 |
| #17987403 | 3 |
| C92×C19⋊C3 | 3 |
| C3×C92×C19 | 3 |
| C9×#737 | 19 |