Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 482 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 |
|---|---|---|
| 1. #20277366 | C2 | semidirect |
| 4. #20273162 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 24. C53×#477 | C4 | semidirect |
| 25. C53×#460 | C4 | semidirect |
| 191. #477 | Dic53 | semidirect |
| 192. #460 | Dic53 | semidirect |
| 209. C53 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277366 | 2 |
| #20275635 | 2 |
| #20273223 | 2 |
| #20273162 | 2 |
| #20272607 | 2 |
| #20272572 | 2 |
| C53×#3112 | 2 |
| #9330 | 53 |