Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291684 | C2 | semidirect |
| 2. #20291024 | C2 | semidirect |
| 3. #20290598 | C2 | semidirect |
| 4. #20289782 | C2 | semidirect |
| 17. #16810877 | C4 | semidirect |
| 18. #16810876 | C4 | semidirect |
| 19. #16810873 | C4 | semidirect |
| 24. C53×#469 | C4 | semidirect |
| 31. D53⋊C16 | D4 | semidirect |
| 200. #469 | #6157 | semidirect |
| 209. C53 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291684 | 2 |
| #20291024 | 2 |
| #20290598 | 2 |
| #20289782 | 2 |
| #20284361 | 2 |
| #13074 | 53 |