Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1482 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 184 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. #20290605 | C2 | semidirect |
| 2. C2×#16811466 | C2 | semidirect |
| 36. C22×D4×C53 | C8 | semidirect |
| 168. C53 | #8302 | semidirect |
| 174. C22×D4 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290605 | 2 |
| C2×#16811466 | 2 |
| C22×D4×Dic53 | 2 |
| #8302 | 53 |