Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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. #17987415 | C3 | semidirect |
| 4. C3×#13095305 | C3 | semidirect |
| 5. #17987347 | C3 | semidirect |
| 6. #17987345 | C3 | semidirect |
| 8. #17987336 | C3 | semidirect |
| 15. #13095316 | C9 | semidirect |
| 36. #10587025 | C3×C9 | semidirect |
| 46. C3×#4294 | C3×C9 | semidirect |
| 122. C19 | #731⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095316 | 3 |
| #17987415 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| C3×#13095305 | 3 |
| #17987347 | 3 |
| #17987345 | 3 |
| H(3,𝔽3)⋊#4294 | 3 |
| #17987336 | 3 |
| C19×H(3,𝔽3)⋊C9 | 3 |
| #731⋊C9 | 19 |