Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1076 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 355 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. #17987472 | C3 | semidirect |
| 3. #17987471 | C3 | semidirect |
| 4. #17987470 | C3 | semidirect |
| 5. #17987469 | C3 | semidirect |
| 6. #17987468 | C3 | semidirect |
| 7. C19⋊C3×C9⋊C9 | C3 | semidirect |
| 8. C92×C19⋊C3 | C3 | semidirect |
| 9. C19×#6900 | C3 | semidirect |
| 19. #13095307 | C32 | semidirect |
| 20. #13095306 | C32 | semidirect |
| 21. #13095305 | C32 | semidirect |
| 22. C9×#4294 | C32 | semidirect |
| 24. C19×C9⋊C9 | C32 | semidirect |
| 25. C92×C19 | C32 | semidirect |
| 44. C9×C19⋊C3 | 3−1+2 | semidirect |
| 51. #6900 | C19⋊C3 | direct (N × H) |
| 61. C9×C19 | C3×3−1+2 | semidirect |
| 64. #4294 | C3×3−1+2 | semidirect |
| 78. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 80. C92 | C3×C19⋊C3 | semidirect |
| 85. C19⋊C3 | #6900 | direct (N × H) |
| 104. C19 | C3×#6900 | semidirect |
| 115. C9 | 3−1+2×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C19⋊C3 | 3 |
| #17987472 | 3 |
| #17987471 | 3 |
| #17987470 | 3 |
| #17987469 | 3 |
| #17987468 | 3 |
| C19⋊C3×C9⋊C9 | 3 |
| C92×C19⋊C3 | 3 |
| C19×#6900 | 3 |
| C3×#6900 | 19 |