Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1166 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 301 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×#13095332 | C3 | semidirect |
| 2. C32×C9×C19⋊C3 | C3 | semidirect |
| 3. #17987432 | C3 | semidirect |
| 4. #17987429 | C3 | semidirect |
| 5. #17987422 | C3 | semidirect |
| 6. #17987418 | C3 | semidirect |
| 8. C9×C32⋊(C19⋊C3) | C3 | semidirect |
| 9. C3×C19×#737 | C3 | semidirect |
| 13. C3×#10587022 | C32 | semidirect |
| 14. C3×#10587023 | C32 | semidirect |
| 21. C3×C9×C19⋊C3 | C32 | semidirect |
| 22. C32⋊#4294 | C32 | semidirect |
| 24. #13095303 | C32 | semidirect |
| 27. C3×C19×3−1+2 | C32 | semidirect |
| 30. C32×C9×C19 | C32 | semidirect |
| 42. C3×C9×C19 | H(3,𝔽3) | semidirect |
| 58. C3×#737 | C19⋊C3 | semidirect |
| 76. C3×C19⋊C3 | #737 | semidirect |
| 89. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 99. C32×C9 | C3×C19⋊C3 | semidirect |
| 130. C3×C9 | C32⋊(C19⋊C3) | semidirect |
| 134. C19 | #10624869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987432 | 3 |
| #17987429 | 3 |
| #17987422 | 3 |
| #17987418 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C3×C19×#737 | 3 |
| #10624869 | 19 |