Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20275548 | C2 | semidirect |
| 2. #20273437 | C2 | semidirect |
| 3. #20273350 | C2 | semidirect |
| 4. #20273223 | C2 | semidirect |
| 6. #16810680 | C22 | semidirect |
| 7. #16810647 | C22 | semidirect |
| 9. #16810469 | C22 | semidirect |
| 16. C53×#555 | C4 | semidirect |
| 18. D42×C53 | C4 | semidirect |
| 162. #555 | Dic53 | semidirect |
| 164. D42 | Dic53 | semidirect |
| 177. C53 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275548 | 2 |
| #20273437 | 2 |
| #20273350 | 2 |
| #20273223 | 2 |
| C53×#3549 | 2 |
| #8491 | 53 |