Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 74 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. D53⋊#365 | C2 | semidirect |
| 4. #20290536 | C2 | semidirect |
| 5. #20289781 | C2 | semidirect |
| 6. #20289761 | C2 | semidirect |
| 23. #16810437 | C4 | semidirect |
| 24. #16810436 | C4 | semidirect |
| 25. #16810435 | C4 | semidirect |
| 26. C53×#361 | C4 | semidirect |
| 184. #361 | #6157 | semidirect |
| 186. C53 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#365 | 2 |
| D53⋊#361 | 2 |
| #20290864 | 2 |
| #20290536 | 2 |
| #20289781 | 2 |
| #20289761 | 2 |
| #361×D53 | 2 |
| #13138 | 53 |