Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #20272890 | C2 | semidirect |
| 4. #20272875 | C2 | semidirect |
| 12. C53×#541 | C4 | semidirect |
| 15. C53×#494 | C4 | semidirect |
| 16. C53×#491 | C4 | semidirect |
| 22. C53×#433 | C4 | semidirect |
| 148. #541 | Dic53 | semidirect |
| 151. #494 | Dic53 | semidirect |
| 152. #491 | Dic53 | semidirect |
| 158. #433 | Dic53 | semidirect |
| 165. C53 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276404 | 2 |
| #20276390 | 2 |
| #20272890 | 2 |
| #20272875 | 2 |
| C53×#3223 | 2 |
| #13608 | 53 |