Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 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×#13095331 | C3 | semidirect |
| 2. C32×#10587023 | C3 | semidirect |
| 3. #17987525 | C3 | direct (N × H) |
| 4. C3×#13095322 | C3 | semidirect |
| 5. C3×#13095316 | C3 | semidirect |
| 6. C3×#13095313 | C3 | semidirect |
| 7. C3×C19×#732 | C3 | semidirect |
| 10. #13095331 | C32 | semidirect |
| 15. C3×#10587023 | C32 | semidirect |
| 19. #13095322 | C32 | semidirect |
| 20. #13095316 | C32 | semidirect |
| 21. #13095313 | C32 | semidirect |
| 24. C19×#732 | C32 | semidirect |
| 53. C3×#732 | C19⋊C3 | semidirect |
| 84. #732 | C3×C19⋊C3 | semidirect |
| 90. C3×C19 | #6913 | semidirect |
| 116. C19 | C3×#6913 | semidirect |
| 135. C3 | #17987525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095331 | 3 |
| C32×#10587023 | 3 |
| #17987525 | 3 |
| C3×#13095322 | 3 |
| C3×#13095316 | 3 |
| C3×#13095313 | 3 |
| C3×C19×#732 | 3 |
| C3×#6913 | 19 |