Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 15. C22×Q16×C53 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 23. C53×#419 | C4 | semidirect |
| 165. C22×Q16 | Dic53 | semidirect |
| 173. #427 | Dic53 | semidirect |
| 174. #419 | Dic53 | semidirect |
| 183. C53 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276410 | 2 |
| #20276369 | 2 |
| #20274765 | 2 |
| #20274515 | 2 |
| C53×#3059 | 2 |
| #13233 | 53 |