Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1058 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 1. C3×#13095333 | C3 | semidirect |
| 2. C3×#13095331 | C3 | semidirect |
| 3. C32×#10587022 | C3 | semidirect |
| 4. #17987432 | C3 | semidirect |
| 5. #17987431 | C3 | semidirect |
| 6. #17987429 | C3 | semidirect |
| 7. #17987428 | C3 | semidirect |
| 8. #17987424 | C3 | semidirect |
| 9. #17987418 | C3 | semidirect |
| 11. C19×#6893 | C3 | semidirect |
| 17. C3×#10587025 | C32 | semidirect |
| 21. C3×#10587022 | C32 | semidirect |
| 22. C3×#10587023 | C32 | semidirect |
| 27. C32×#4294 | C32 | semidirect |
| 28. C3×C9×C19⋊C3 | C32 | semidirect |
| 29. C32⋊#4294 | C32 | semidirect |
| 31. #13095303 | C32 | semidirect |
| 32. #13095303 | C32 | semidirect |
| 36. C19×C32⋊C9 | C32 | semidirect |
| 56. C3×#4294 | H(3,𝔽3) | semidirect |
| 73. #6893 | C19⋊C3 | semidirect |
| 120. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 156. C19 | #10624882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| C3×#13095331 | 3 |
| C32×#10587022 | 3 |
| #17987432 | 3 |
| #17987431 | 3 |
| #17987429 | 3 |
| #17987428 | 3 |
| #17987424 | 3 |
| #17987418 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C19×#6893 | 3 |
| #10624882 | 19 |