Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20289791 | C2 | semidirect |
| 4. #20289781 | C2 | semidirect |
| 15. #16810672 | C4 | semidirect |
| 18. #16810670 | C4 | semidirect |
| 21. C53×#430 | C4 | semidirect |
| 172. #430 | #6157 | semidirect |
| 181. C53 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#349 | 2 |
| #20290593 | 2 |
| #20289791 | 2 |
| #20289781 | 2 |
| #430×D53 | 2 |
| #12875 | 53 |