Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
868 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20274720 | C2 | semidirect |
| 4. C2×Q8⋊#88322 | C2 | semidirect |
| 16. C53×#559 | C4 | semidirect |
| 169. #559 | Dic53 | semidirect |
| 183. C53 | #8445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275522 | 2 |
| #20274720 | 2 |
| C2×#16810367 | 2 |
| C2×Q8⋊#88322 | 2 |
| C2×C53×#559 | 2 |
| #8445 | 53 |