Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20290599 | C2 | semidirect |
| 3. #20289806 | C2 | semidirect |
| 158. C53 | #12809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291008 | 2 |
| #20290599 | 2 |
| #20289806 | 2 |
| #20283428 | 2 |
| #12809 | 53 |