Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C3×#13095305 | C3 | semidirect |
| 5. #17987308 | C3 | semidirect |
| 6. #17987308 | C3 | semidirect |
| 7. #17987308 | C3 | semidirect |
| 8. #17987308 | C3 | semidirect |
| 9. C3×C19×C9⋊C9 | C3 | semidirect |
| 48. C3×C9×C19 | 3−1+2 | semidirect |
| 67. C3×#4294 | 3−1+2 | semidirect |
| 71. C3×C9⋊C9 | C19⋊C3 | semidirect |
| 170. C3×C9 | #10587023 | semidirect |
| 172. C19 | #10624565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587023 | 3 |
| C3×#13095305 | 3 |
| C3×#13095303 | 3 |
| #17987308 | 3 |
| C3×C19×C9⋊C9 | 3 |
| #10624565 | 19 |