Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1258 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 3. #20275557 | C2 | semidirect |
| 120. C2×Dic53 | #101 | semidirect |
| 168. C53 | #21799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133215 | 2 |
| #20283344 | 2 |
| #20275557 | 2 |
| #20274639 | 2 |
| #20274638 | 2 |
| C53×#1784 | 2 |
| #21799 | 53 |