Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20290921 | C2 | semidirect |
| 2. #20290275 | C2 | semidirect |
| 3. #20289675 | C2 | semidirect |
| 4. #20289674 | C2 | semidirect |
| 160. C53 | #11682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290921 | 2 |
| #20290275 | 2 |
| #20289675 | 2 |
| #20289674 | 2 |
| #20285286 | 2 |
| #11682 | 53 |