Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
314 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 52 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. #17987435 | C3 | semidirect |
| 3. #17987427 | C3 | semidirect |
| 4. 3−1+2×#4294 | C3 | semidirect |
| 5. #17987321 | C3 | semidirect |
| 6. #17987321 | C3 | semidirect |
| 7. #17987318 | C3 | semidirect |
| 8. #17987315 | C3 | semidirect |
| 9. #17987315 | C3 | semidirect |
| 10. #17987311 | C3 | semidirect |
| 11. #17987311 | C3 | semidirect |
| 13. C19×#6857 | C3 | semidirect |
| 79. #6857 | C19⋊C3 | semidirect |
| 167. C19 | #10624613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095331 | 3 |
| #17987435 | 3 |
| #17987427 | 3 |
| 3−1+2×#4294 | 3 |
| #17987321 | 3 |
| #17987318 | 3 |
| #17987315 | 3 |
| #17987311 | 3 |
| #17987309 | 3 |
| C19×#6857 | 3 |
| #10624613 | 19 |