Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. #20290231 | C2 | semidirect |
| 3. D53⋊#333 | C2 | semidirect |
| 5. #20289605 | C2 | semidirect |
| 6. #20289584 | C2 | semidirect |
| 236. C53 | #9170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291414 | 2 |
| #20290231 | 2 |
| D53⋊#333 | 2 |
| #20290013 | 2 |
| #20289605 | 2 |
| #20289584 | 2 |
| #20284525 | 2 |
| #9170 | 53 |