Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20290600 | C2 | semidirect |
| 3. #20290598 | C2 | semidirect |
| 4. #20289815 | C2 | semidirect |
| 15. C22×C8×D53 | C4 | semidirect |
| 22. #16810586 | C4 | semidirect |
| 23. #16810579 | C4 | semidirect |
| 24. C53×#424 | C4 | semidirect |
| 201. #424 | #6157 | semidirect |
| 211. C53 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290968 | 2 |
| #20290600 | 2 |
| #20290598 | 2 |
| #20289815 | 2 |
| #20283408 | 2 |
| #12805 | 53 |