Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
992 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 292 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×#13095332 | C3 | semidirect |
| 2. C32×#10587023 | C3 | semidirect |
| 3. #17987523 | C3 | direct (N × H) |
| 4. C3×#13095321 | C3 | semidirect |
| 5. C3×#13095319 | C3 | semidirect |
| 6. C3×#13095318 | C3 | semidirect |
| 7. C3×#13095316 | C3 | semidirect |
| 8. C3×#13095315 | C3 | semidirect |
| 9. C3×#13095313 | C3 | semidirect |
| 10. C3×C19×#737 | C3 | semidirect |
| 13. #13095332 | C32 | semidirect |
| 21. C3×#10587023 | C32 | semidirect |
| 26. #13095321 | C32 | semidirect |
| 27. #13095319 | C32 | semidirect |
| 28. #13095318 | C32 | semidirect |
| 29. #13095316 | C32 | semidirect |
| 30. #13095315 | C32 | semidirect |
| 31. #13095313 | C32 | semidirect |
| 33. C19×#737 | C32 | semidirect |
| 78. C3×#737 | C19⋊C3 | semidirect |
| 110. #737 | C3×C19⋊C3 | semidirect |
| 137. C3×C19 | #6913 | semidirect |
| 178. C19 | C3×#6913 | semidirect |
| 203. C3 | #17987523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| C32×#10587023 | 3 |
| #17987523 | 3 |
| C3×#13095321 | 3 |
| C3×#13095319 | 3 |
| C3×#13095318 | 3 |
| C3×#13095316 | 3 |
| C3×#13095315 | 3 |
| C3×#13095313 | 3 |
| C3×C19×#737 | 3 |
| C3×#6913 | 19 |