Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#16811542 | C2 | semidirect |
| 4. #20289789 | C2 | semidirect |
| 165. C22×C53 | #362 | semidirect |
| 217. C53 | #13003 | semidirect |
| 366. C22 | #16811542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133287 | 2 |
| C2×#16811542 | 2 |
| #20290943 | 2 |
| #20289789 | 2 |
| #467×D53 | 2 |
| #13003 | 53 |