Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1166 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1166 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×#13095333 | C3 | semidirect |
| 2. C33×#4294 | C3 | semidirect |
| 3. #17987432 | C3 | semidirect |
| 4. #17987428 | C3 | semidirect |
| 5. #17987427 | C3 | semidirect |
| 6. #17987421 | C3 | semidirect |
| 8. #17987406 | C3 | semidirect |
| 9. C19×#6891 | C3 | semidirect |
| 12. C3×#10587022 | C32 | semidirect |
| 13. C3×#10587023 | C32 | semidirect |
| 22. C3×C9×C19⋊C3 | C32 | semidirect |
| 24. #13095303 | C32 | semidirect |
| 43. C3×#4294 | H(3,𝔽3) | semidirect |
| 58. #6891 | C19⋊C3 | semidirect |
| 66. C32×C19 | #737 | semidirect |
| 122. C19 | #10624869 | semidirect |
| 130. C32 | #13095333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| C33×#4294 | 3 |
| #17987432 | 3 |
| #17987428 | 3 |
| #17987427 | 3 |
| #17987421 | 3 |
| #17987417 | 3 |
| #17987406 | 3 |
| C19×#6891 | 3 |
| #10624869 | 19 |