Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20287817 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. #20274762 | C2 | semidirect |
| 5. #20272830 | C2 | semidirect |
| 6. #20272829 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 41. #13133157 | D4 | semidirect |
| 62. M32×C53 | D4 | semidirect |
| 166. C2×#361 | D53 | semidirect |
| 194. C53 | #13079 | semidirect |
| 222. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284359 | 2 |
| C2×#16810436 | 2 |
| #20274762 | 2 |
| #20272830 | 2 |
| #20272829 | 2 |
| C2×C53×#361 | 2 |
| #13079 | 53 |