Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276400 | C2 | semidirect |
| 2. #20276380 | C2 | semidirect |
| 3. #20272875 | C2 | semidirect |
| 4. #20272872 | C2 | semidirect |
| 14. C53×#532 | C4 | semidirect |
| 17. C53×#497 | C4 | semidirect |
| 20. C53×#496 | C4 | semidirect |
| 22. C2×#97×C53 | C4 | semidirect |
| 180. #532 | Dic53 | semidirect |
| 183. #497 | Dic53 | semidirect |
| 186. #496 | Dic53 | semidirect |
| 190. C2×#97 | Dic53 | semidirect |
| 195. C53 | #13577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276400 | 2 |
| #20276380 | 2 |
| #20272875 | 2 |
| #20272872 | 2 |
| C53×#3150 | 2 |
| #13577 | 53 |