Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
854 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20289810 | C2 | semidirect |
| 6. #16811602 | C4 | semidirect |
| 10. C22×C4×Dic53 | C4 | semidirect |
| 11. #16810528 | C4 | semidirect |
| 15. C2×#117×C53 | C4 | semidirect |
| 22. #13133276 | C2×C4 | semidirect |
| 175. C2×#117 | #6157 | semidirect |
| 185. C53 | #12581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811602 | 2 |
| #20289810 | 2 |
| #20277203 | 2 |
| #12581 | 53 |