Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
786 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20273056 | C2 | semidirect |
| 3. #20272711 | C2 | semidirect |
| 4. C4×#99×C53 | C2 | semidirect |
| 5. C23×D212 | C4 | semidirect |
| 9. #16810540 | C4 | semidirect |
| 12. #16810483 | C4 | semidirect |
| 15. #16810347 | C22 | semidirect |
| 19. C53×#342 | C22 | semidirect |
| 186. C4×#99 | D53 | semidirect |
| 209. #342 | C2×D53 | semidirect |
| 212. C53 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278071 | 2 |
| #20273056 | 2 |
| #20272711 | 2 |
| C4×#99×C53 | 2 |
| #11772 | 53 |