Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. C22×#11719908 | C4 | semidirect |
| 14. C53×C22⋊C16 | C4 | semidirect |
| 55. C22⋊Dic53 | C16 | semidirect |
| 130. C22⋊C16 | Dic53 | semidirect |
| 132. C53 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11719908 | 2 |
| C8×C22⋊Dic53 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #7199 | 53 |