Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 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⋊#504 | C2 | semidirect |
| 2. #20291036 | C2 | semidirect |
| 3. C2×#16811537 | C2 | semidirect |
| 4. #20290602 | C2 | semidirect |
| 5. #20289794 | C2 | semidirect |
| 6. #20289778 | C2 | semidirect |
| 25. #16810899 | C4 | semidirect |
| 26. #16810898 | C4 | semidirect |
| 27. #16810890 | C4 | semidirect |
| 32. C53×#472 | C4 | semidirect |
| 239. #472 | #6157 | semidirect |
| 251. C53 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#504 | 2 |
| #20291036 | 2 |
| C2×#16811537 | 2 |
| #20290602 | 2 |
| #20289794 | 2 |
| #20289778 | 2 |
| #20284433 | 2 |
| #13071 | 53 |