Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×#16810440 | C2 | semidirect |
| 4. #20275630 | C2 | semidirect |
| 6. #20272809 | C2 | semidirect |
| 7. C53×#2151 | C2 | semidirect |
| 150. #2151 | D53 | semidirect |
| 178. C53 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C2×#16810440 | 2 |
| C2×#16810437 | 2 |
| #20275630 | 2 |
| #20275625 | 2 |
| #20272809 | 2 |
| C53×#2151 | 2 |
| #13440 | 53 |