Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊#430 | C2 | semidirect |
| 2. #20291030 | C2 | semidirect |
| 3. D53⋊#349 | C2 | semidirect |
| 4. #20289797 | C2 | semidirect |
| 36. #13133288 | D4 | semidirect |
| 221. C53 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#430 | 2 |
| #20291030 | 2 |
| D53⋊#349 | 2 |
| #20289797 | 2 |
| #20284322 | 2 |
| #12998 | 53 |