Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q32×Dic53 | C2 | semidirect |
| 3. #20272915 | C2 | semidirect |
| 4. #20272896 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 18. C53×SD64 | C4 | semidirect |
| 32. Q32×C53 | C2×C4 | semidirect |
| 36. C32×C53 | C2×C4 | semidirect |
| 97. SD64 | Dic53 | semidirect |
| 105. C53 | #13652 | semidirect |
| 111. Q32 | C2×Dic53 | semidirect |
| 122. C32 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic53 | 2 |
| D16×Dic53 | 2 |
| #20272915 | 2 |
| #20272896 | 2 |
| #20272893 | 2 |
| #20272848 | 2 |
| C2×C53×SD64 | 2 |
| #13652 | 53 |