Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 420 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. C2×#16810420 | C2 | semidirect |
| 2. C2×#16810418 | C2 | semidirect |
| 3. #20272875 | C2 | semidirect |
| 4. #20272872 | C2 | semidirect |
| 14. C53×#532 | C4 | semidirect |
| 16. C53×#497 | C4 | semidirect |
| 18. C53×#496 | C4 | semidirect |
| 22. C4×M16×C53 | C4 | semidirect |
| 45. C4⋊Q8×C53 | C2×C4 | semidirect |
| 46. #127×C53 | C2×C4 | semidirect |
| 57. #97×C53 | C2×C4 | semidirect |
| 58. #97×C53 | C2×C4 | semidirect |
| 184. #532 | Dic53 | semidirect |
| 186. #497 | Dic53 | semidirect |
| 188. #496 | Dic53 | semidirect |
| 194. C4×M16 | Dic53 | semidirect |
| 199. C53 | #13578 | semidirect |
| 217. C4⋊Q8 | C2×Dic53 | semidirect |
| 218. #127 | C2×Dic53 | semidirect |
| 234. #97 | C2×Dic53 | semidirect |
| 235. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| C2×#16810418 | 2 |
| #20272875 | 2 |
| #20272872 | 2 |
| C53×#3153 | 2 |
| #13578 | 53 |