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. #17987528 | C3 | direct (N × H) |
| 3. C3×#13095322 | C3 | semidirect |
| 4. C3×#13095320 | C3 | semidirect |
| 5. C3×#13095317 | C3 | semidirect |
| 6. C3×#13095314 | C3 | semidirect |
| 7. C32×C19×3−1+2 | C3 | semidirect |
| 9. #13095332 | C32 | semidirect |
| 15. #13095322 | C32 | semidirect |
| 16. #13095320 | C32 | semidirect |
| 17. #13095317 | C32 | semidirect |
| 18. #13095314 | C32 | semidirect |
| 22. C3×C19×3−1+2 | C32 | semidirect |
| 52. C32×3−1+2 | C19⋊C3 | semidirect |
| 80. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 93. C3×C19 | #6913 | semidirect |
| 120. C19 | C3×#6913 | semidirect |
| 139. C3 | #17987528 | 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 |
| #17987528 | 3 |
| C3×#13095322 | 3 |
| C3×#13095320 | 3 |
| C3×#13095317 | 3 |
| C3×#13095314 | 3 |
| C32×C19×3−1+2 | 3 |
| C3×#6913 | 19 |