Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×#13133132 | C2 | semidirect |
| 2. #20273056 | C2 | semidirect |
| 3. #20272712 | C2 | semidirect |
| 8. #16810390 | C22 | semidirect |
| 10. #16810347 | C22 | semidirect |
| 11. C23×D4×C53 | C4 | semidirect |
| 15. C53×#394 | C4 | semidirect |
| 18. C53×#380 | C4 | semidirect |
| 197. C23×D4 | Dic53 | semidirect |
| 203. #394 | Dic53 | semidirect |
| 206. #380 | Dic53 | semidirect |
| 212. C53 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133132 | 2 |
| #20273056 | 2 |
| #20272712 | 2 |
| C53×#2408 | 2 |
| #11772 | 53 |