Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1064 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1064 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. C32×C9×C19⋊C3 | C3 | semidirect |
| 3. #17987501 | C3 | direct (N × H) |
| 4. C3×#13095322 | C3 | semidirect |
| 5. C3×#13095320 | C3 | semidirect |
| 6. C3×#13095318 | C3 | semidirect |
| 7. C3×#13095315 | C3 | semidirect |
| 8. C3×C19×#733 | C3 | semidirect |
| 11. #13095333 | C32 | semidirect |
| 23. C3×C9×C19⋊C3 | C32 | semidirect |
| 24. #13095322 | C32 | semidirect |
| 25. #13095320 | C32 | semidirect |
| 26. #13095318 | C32 | semidirect |
| 27. #13095315 | C32 | semidirect |
| 30. C19×#733 | C32 | semidirect |
| 67. C3×#733 | C19⋊C3 | semidirect |
| 106. #733 | C3×C19⋊C3 | semidirect |
| 112. C3×C19 | #6908 | semidirect |
| 147. C19 | C3×#6908 | semidirect |
| 169. C3 | #17987501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987501 | 3 |
| C3×#13095322 | 3 |
| C3×#13095320 | 3 |
| C3×#13095318 | 3 |
| C3×#13095315 | 3 |
| C3×C19×#733 | 3 |
| C3×#6908 | 19 |