Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283702 | C2 | semidirect |
| 2. #20273292 | C2 | semidirect |
| 3. #20273262 | C2 | semidirect |
| 4. #20273132 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 26. C53×#497 | C4 | semidirect |
| 27. C53×#496 | C4 | semidirect |
| 28. C53×#491 | C4 | semidirect |
| 29. C53×#490 | C4 | semidirect |
| 214. #497 | Dic53 | semidirect |
| 215. #496 | Dic53 | semidirect |
| 216. #491 | Dic53 | semidirect |
| 217. #490 | Dic53 | semidirect |
| 239. C53 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283702 | 2 |
| #20273292 | 2 |
| #20273262 | 2 |
| #20273132 | 2 |
| #20272581 | 2 |
| #20272576 | 2 |
| C53×#3219 | 2 |
| #9370 | 53 |