Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
980 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 271 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. #17987519 | C3 | semidirect |
| 4. #17987518 | C3 | semidirect |
| 5. #17987517 | C3 | semidirect |
| 6. #17987516 | C3 | semidirect |
| 7. C19⋊C3×#733 | C3 | semidirect |
| 8. C19×#6912 | C3 | semidirect |
| 30. #13095322 | C32 | semidirect |
| 31. #13095321 | C32 | semidirect |
| 34. C19×#733 | C32 | semidirect |
| 76. #6912 | C19⋊C3 | direct (N × H) |
| 121. #733 | C3×C19⋊C3 | semidirect |
| 129. C19⋊C3 | #6912 | direct (N × H) |
| 164. C19 | C3×#6912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C19⋊C3 | 3 |
| #17987519 | 3 |
| #17987518 | 3 |
| #17987517 | 3 |
| #17987516 | 3 |
| C19⋊C3×#733 | 3 |
| C19×#6912 | 3 |
| C3×#6912 | 19 |