Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×D53⋊M32 | C2 | semidirect |
| 2. C2×#16811541 | C2 | semidirect |
| 3. #20290594 | C2 | semidirect |
| 4. #20289789 | C2 | semidirect |
| 27. #13133292 | D4 | semidirect |
| 174. C2×D53 | #361 | semidirect |
| 215. C53 | #13067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊M32 | 2 |
| C2×#16811541 | 2 |
| #20290594 | 2 |
| #20289789 | 2 |
| #466×D53 | 2 |
| #13067 | 53 |