Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20274920 | C2 | semidirect |
| 5. #20272601 | C2 | semidirect |
| 6. #20272562 | C2 | semidirect |
| 7. C53×#1851 | C2 | semidirect |
| 22. #16810359 | C4 | semidirect |
| 23. #16810359 | C4 | semidirect |
| 24. #16810356 | C4 | semidirect |
| 25. #16810356 | C4 | semidirect |
| 213. #1851 | D53 | semidirect |
| 248. C53 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283760 | 2 |
| #20275017 | 2 |
| #20274920 | 2 |
| #20273204 | 2 |
| #20272601 | 2 |
| #20272562 | 2 |
| C53×#1851 | 2 |
| #8875 | 53 |