Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
932 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 346 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. #17987440 | C3 | direct (N × H) |
| 4. C3×#13095307 | C3 | semidirect |
| 5. C3×#13095305 | C3 | semidirect |
| 6. C3×#13095305 | C3 | semidirect |
| 18. #13095307 | C32 | semidirect |
| 19. #13095305 | C32 | semidirect |
| 20. #13095305 | C32 | semidirect |
| 40. C3×#4294 | 3−1+2 | semidirect |
| 69. #4294 | C3×3−1+2 | semidirect |
| 87. C3×C19 | #6894 | semidirect |
| 112. C19 | C3×#6894 | semidirect |
| 130. C3 | #17987440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C33×#4294 | 3 |
| #17987440 | 3 |
| C3×#13095307 | 3 |
| C3×#13095305 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×C19×C32⋊C9 | 3 |
| C3×#6894 | 19 |