Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20289676 | C2 | semidirect |
| 4. #20289675 | C2 | semidirect |
| 165. C53 | #11668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20290276 | 2 |
| #20289676 | 2 |
| #20289675 | 2 |
| C4×Q16×D53 | 2 |
| #11668 | 53 |