Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 192 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. #20290327 | C2 | semidirect |
| 68. D53⋊C8 | Q16 | semidirect |
| 149. C53 | #17977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291504 | 2 |
| #20290327 | 2 |
| #20290274 | 2 |
| #20290065 | 2 |
| #20289911 | 2 |
| #20285302 | 2 |
| #17977 | 53 |