Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1166 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 310 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. #17987431 | C3 | semidirect |
| 3. #17987426 | C3 | semidirect |
| 4. #17987425 | C3 | semidirect |
| 5. #17987421 | C3 | semidirect |
| 7. C9×C32⋊(C19⋊C3) | C3 | semidirect |
| 8. C33×C9×C19 | C3 | semidirect |
| 11. C3×#10587022 | C32 | semidirect |
| 12. C3×#10587023 | C32 | semidirect |
| 15. C3×C9×C19⋊C3 | C32 | semidirect |
| 17. #13095303 | C32 | semidirect |
| 35. C3×C9×C19 | H(3,𝔽3) | semidirect |
| 48. C33×C9 | C19⋊C3 | semidirect |
| 60. C32×C19 | #737 | semidirect |
| 106. C3×C9 | C32⋊(C19⋊C3) | semidirect |
| 111. C19 | #10624869 | semidirect |
| 119. C32 | #13095332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| #17987431 | 3 |
| #17987426 | 3 |
| #17987425 | 3 |
| #17987421 | 3 |
| #17987417 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C33×C9×C19 | 3 |
| #10624869 | 19 |