Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20291063 | C2 | semidirect |
| 4. #20290524 | C2 | semidirect |
| 5. #20289784 | C2 | semidirect |
| 6. #20289761 | C2 | semidirect |
| 23. #16810440 | C4 | semidirect |
| 24. #16810438 | C4 | semidirect |
| 25. #16810436 | C4 | semidirect |
| 26. C53×#361 | C4 | semidirect |
| 174. #361 | #6157 | semidirect |
| 178. C53 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291063 | 2 |
| #20291036 | 2 |
| #20290870 | 2 |
| #20290524 | 2 |
| #20289784 | 2 |
| #20289761 | 2 |
| #20276461 | 2 |
| #13140 | 53 |