Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
556 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#13133158 | C2 | semidirect |
| 2. C2×#16810893 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. #20276329 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C2×C53×#472 | C2 | semidirect |
| 193. C2×#472 | D53 | semidirect |
| 226. C53 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133158 | 2 |
| C2×#16810893 | 2 |
| C2×#16810436 | 2 |
| C2×#16810435 | 2 |
| #20276329 | 2 |
| #20272808 | 2 |
| C2×C53×#472 | 2 |
| #13313 | 53 |