Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
906 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 116 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×#16811542 | C2 | semidirect |
| 155. C22×C53 | #362 | semidirect |
| 162. C2×D53 | #362 | semidirect |
| 198. C53 | #12737 | semidirect |
| 338. C22 | #16811542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811542 | 2 |
| #20290943 | 2 |
| #20290594 | 2 |
| C22×Q16×D53 | 2 |
| #12737 | 53 |