Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275548 | C2 | semidirect |
| 3. #20273438 | C2 | semidirect |
| 4. #20273224 | C2 | semidirect |
| 5. C53×#1536 | C2 | semidirect |
| 7. #16811339 | C4 | semidirect |
| 10. #16811258 | C4 | semidirect |
| 14. #16810647 | C22 | semidirect |
| 16. #16810469 | C22 | semidirect |
| 21. C53×#432 | C22 | semidirect |
| 153. #1536 | D53 | semidirect |
| 169. #432 | C2×D53 | semidirect |
| 177. C53 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20275548 | 2 |
| #20273438 | 2 |
| #20273224 | 2 |
| C53×#1536 | 2 |
| #8491 | 53 |