Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 7034 conjugacy classes of subgroups — too many to draw. Only its 675 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. C25×Dic53 | C2 | semidirect |
| 3. C2×#16810500 | C2 | semidirect |
| 4. #20272937 | C2 | semidirect |
| 5. C2×C53×#379 | C2 | semidirect |
| 12. C2×#13133186 | C4 | semidirect |
| 14. C22×#11719921 | C22 | semidirect |
| 16. C2×#13133124 | C22 | semidirect |
| 25. C22×C22⋊D53 | C2×C4 | semidirect |
| 31. C23×Dic53 | D4 | semidirect |
| 37. C2×C22⋊Dic53 | C2×C4 | semidirect |
| 58. C24×C53 | C22⋊C4 | semidirect |
| 69. C23×D53 | C22×C4 | semidirect |
| 89. C22×Dic53 | C22×C4 | semidirect |
| 135. C2×Dic53 | #120 | semidirect |
| 144. C22×C53 | #386 | semidirect |
| 163. C2×#379 | D53 | semidirect |
| 186. C53 | #14694 | semidirect |
| 230. C24 | #11719921 | semidirect |
| 315. C22 | #16810500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic53 | 2 |
| C22×#13133186 | 2 |
| C2×#16810500 | 2 |
| #20272937 | 2 |
| C2×C53×#379 | 2 |
| #14694 | 53 |