Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20289923 | C2 | semidirect |
| 4. #20289600 | C2 | semidirect |
| 167. C53 | #8243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291439 | 2 |
| #20290219 | 2 |
| #20289923 | 2 |
| #20289600 | 2 |
| #20273305 | 2 |
| #8243 | 53 |