Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4614 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 667 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. C2×C4×C22⋊Dic53 | C2 | semidirect |
| 2. #20272986 | C2 | semidirect |
| 3. #20272956 | C2 | semidirect |
| 10. C22×#41×C53 | C4 | semidirect |
| 46. C22×C4×C53 | C22⋊C4 | semidirect |
| 53. C22×Dic53 | #41 | semidirect |
| 100. C22×#41 | Dic53 | semidirect |
| 108. C53 | #13851 | semidirect |
| 144. C22×C4 | C22⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic53 | 2 |
| #20272986 | 2 |
| #20272956 | 2 |
| C23×#41×C53 | 2 |
| #13851 | 53 |