Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
960 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20275529 | C2 | semidirect |
| 3. C2×#16810363 | C2 | semidirect |
| 4. C2×#16810362 | C2 | semidirect |
| 5. C53×#1959 | C2 | semidirect |
| 8. #16811365 | C4 | semidirect |
| 16. C2×#13133128 | C22 | semidirect |
| 22. C2×#97×C53 | C22 | semidirect |
| 23. C53×#384 | C22 | semidirect |
| 194. #1959 | D53 | semidirect |
| 218. C2×#97 | C2×D53 | semidirect |
| 219. #384 | C2×D53 | semidirect |
| 222. C53 | #8506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811365 | 2 |
| #20275529 | 2 |
| C2×#16810363 | 2 |
| C2×#16810362 | 2 |
| C53×#1959 | 2 |
| #8506 | 53 |