Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
702 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 86 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. C22×#13133278 | C2 | semidirect |
| 2. C2×#16811531 | C2 | semidirect |
| 3. #20290549 | C2 | semidirect |
| 4. #20289813 | C2 | semidirect |
| 36. #13133278 | D4 | semidirect |
| 211. C22×C53 | #355 | semidirect |
| 257. C53 | #13092 | semidirect |
| 443. C22 | #16811531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133278 | 2 |
| C2×#16811531 | 2 |
| #20290549 | 2 |
| #20289813 | 2 |
| #20278374 | 2 |
| #13092 | 53 |