Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 1. C2×#16811545 | C2 | semidirect |
| 3. #20289760 | C2 | semidirect |
| 110. C22×C53 | #364 | semidirect |
| 141. C53 | #12788 | semidirect |
| 235. C22 | #16811545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811545 | 2 |
| #20290942 | 2 |
| #20289760 | 2 |
| C22×C8×Dic53 | 2 |
| #12788 | 53 |