Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 92 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. D53⋊#362 | C2 | semidirect |
| 3. C2×#16811536 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289774 | C2 | semidirect |
| 25. #16810899 | C4 | semidirect |
| 26. #16810898 | C4 | semidirect |
| 29. #16810895 | C4 | semidirect |
| 32. C53×#473 | C4 | semidirect |
| 243. #473 | #6157 | semidirect |
| 253. C53 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#504 | 2 |
| D53⋊#362 | 2 |
| C2×#16811536 | 2 |
| #20290604 | 2 |
| #20289791 | 2 |
| #20289774 | 2 |
| #473×D53 | 2 |
| #13072 | 53 |