Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
926 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 926 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 |
|---|---|---|
| 2. #17987427 | C3 | semidirect |
| 3. #17987426 | C3 | semidirect |
| 4. #17987419 | C3 | semidirect |
| 5. C3×C32⋊#4294 | C3 | semidirect |
| 6. C3×C19×C32⋊C9 | C3 | semidirect |
| 8. C3×#10587023 | C32 | semidirect |
| 12. C32×#4294 | C32 | semidirect |
| 14. C32⋊#4294 | C32 | semidirect |
| 15. C32⋊#4294 | C32 | semidirect |
| 16. #13095303 | C32 | semidirect |
| 18. C32×C9×C19 | C32 | semidirect |
| 20. C19×C32⋊C9 | C32 | semidirect |
| 24. C33×C19 | 3−1+2 | semidirect |
| 44. C3×C32⋊C9 | C19⋊C3 | semidirect |
| 69. C32×C9 | C3×C19⋊C3 | semidirect |
| 75. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 89. C33 | #10587023 | semidirect |
| 100. C19 | #10624883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C19⋊C3) | 3 |
| #17987427 | 3 |
| #17987426 | 3 |
| #17987419 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×C19×C32⋊C9 | 3 |
| #10624883 | 19 |