Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#16810422 | C2 | semidirect |
| 3. #20272870 | C2 | direct (N × H) |
| 4. C2×C53×#333 | C2 | semidirect |
| 15. #16810422 | C22 | semidirect |
| 19. C53×#333 | C22 | semidirect |
| 168. C2×#333 | D53 | semidirect |
| 172. C2×C53 | #1405 | semidirect |
| 189. #333 | C2×D53 | semidirect |
| 190. C53 | C2×#1405 | semidirect |
| 339. C2 | #20272870 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810805 | 2 |
| C2×#16810422 | 2 |
| #20272870 | 2 |
| C2×C53×#333 | 2 |
| C2×#1405 | 53 |