Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 124 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. #20290916 | C2 | semidirect |
| 3. C4×#13133286 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 9. #16811535 | C4 | semidirect |
| 15. C4×D424 | C4 | semidirect |
| 16. D8×Dic53 | C4 | semidirect |
| 17. #16810705 | C4 | semidirect |
| 23. C4×D8×C53 | C4 | semidirect |
| 27. D53⋊C16 | C2×C4 | semidirect |
| 30. #13133286 | C2×C4 | semidirect |
| 81. D8×C53 | C42 | semidirect |
| 99. D424 | C42 | semidirect |
| 186. C4×D8 | #6157 | semidirect |
| 196. C53 | #12637 | semidirect |
| 254. D8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811535 | 2 |
| #20290916 | 2 |
| C4×#13133286 | 2 |
| #20289772 | 2 |
| C4×D8×D53 | 2 |
| #12637 | 53 |