Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291620 | C2 | semidirect |
| 2. #20290107 | C2 | semidirect |
| 5. #20289572 | C2 | semidirect |
| 6. #20289538 | C2 | semidirect |
| 22. #16811003 | C4 | semidirect |
| 23. #16810995 | C4 | semidirect |
| 24. #16810975 | C4 | semidirect |
| 28. C53×#486 | C4 | semidirect |
| 180. #486 | #6157 | semidirect |
| 196. C53 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291620 | 2 |
| #20290107 | 2 |
| #20290104 | 2 |
| #20290075 | 2 |
| #20289572 | 2 |
| #20289538 | 2 |
| #20285672 | 2 |
| #9282 | 53 |