Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 3. #20290930 | C2 | semidirect |
| 4. #20289758 | C2 | semidirect |
| 15. #16811520 | C4 | semidirect |
| 16. #16811519 | C4 | semidirect |
| 21. #16810405 | C4 | semidirect |
| 22. #16810404 | C4 | semidirect |
| 23. C53×#349 | C4 | semidirect |
| 38. #13133291 | C2×C4 | semidirect |
| 54. #13133157 | C2×C4 | semidirect |
| 58. M32×C53 | C2×C4 | semidirect |
| 188. #349 | #6157 | semidirect |
| 191. C53 | #12607 | semidirect |
| 218. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#6157 | 2 |
| D53⋊#349 | 2 |
| #20290930 | 2 |
| #20289758 | 2 |
| #349×D53 | 2 |
| #12607 | 53 |