Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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. 3−1+2×#4296 | C3 | semidirect |
| 3. C3×#13095339 | C3 | semidirect |
| 4. 3−1+2⋊#4296 | C3 | semidirect |
| 6. #17987559 | C3 | semidirect |
| 22. #13095318 | C9 | semidirect |
| 23. #13095317 | C9 | semidirect |
| 24. #13095316 | C9 | semidirect |
| 25. C19×#731 | C9 | semidirect |
| 37. C19×3−1+2 | C3×C9 | semidirect |
| 39. C3×C9×C19 | C3×C9 | semidirect |
| 42. #10587025 | C3×C9 | semidirect |
| 43. C3×#4294 | C3×C9 | semidirect |
| 83. #731 | #4296 | semidirect |
| 104. 3−1+2 | C3×#4296 | semidirect |
| 120. C3×C9 | C3×#4296 | semidirect |
| 121. C19 | #731⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#4296 | 3 |
| H(3,𝔽3)×#4296 | 3 |
| C3×#13095339 | 3 |
| 3−1+2⋊#4296 | 3 |
| H(3,𝔽3)⋊#4296 | 3 |
| #17987559 | 3 |
| C19⋊C3×#731 | 3 |
| #731⋊C9 | 19 |