Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 11. #16810463 | C4 | semidirect |
| 78. Dic53 | Q64 | semidirect |
| 101. C53 | C4×Q64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| Q32×Dic53 | 2 |
| #20276573 | 2 |
| #20272914 | 2 |
| #20272897 | 2 |
| C32×Dic53 | 2 |
| C53×#1416 | 2 |
| C4×Q64 | 53 |