Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20277901 | C2 | semidirect |
| 3. C2×#16810365 | C2 | semidirect |
| 4. #20272597 | C2 | semidirect |
| 17. C53×#490 | C4 | semidirect |
| 144. #490 | Dic53 | semidirect |
| 155. C53 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277901 | 2 |
| #20275540 | 2 |
| C2×#16810365 | 2 |
| #20272597 | 2 |
| C2×C53×#490 | 2 |
| #9002 | 53 |