Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
586 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16811058 | C2 | semidirect |
| 2. C22×#13133158 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. C2×#16810430 | C2 | semidirect |
| 5. #20275625 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#3155 | C2 | semidirect |
| 37. C2×D424 | D4 | semidirect |
| 43. #13133157 | D4 | semidirect |
| 47. C2×#11719908 | D4 | semidirect |
| 202. #3155 | D53 | semidirect |
| 237. C53 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C22×#13133158 | 2 |
| C2×#16810436 | 2 |
| C2×#16810430 | 2 |
| #20275625 | 2 |
| #20272804 | 2 |
| C53×#3155 | 2 |
| #13336 | 53 |