Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
282 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 9. #16811486 | C4 | semidirect |
| 12. C4×#11719908 | C4 | semidirect |
| 14. C4×C16×C53 | C4 | semidirect |
| 19. #13133286 | C8 | semidirect |
| 111. C4×C16 | #6157 | semidirect |
| 115. C53 | #7171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133286 | 2 |
| D53⋊#335 | 2 |
| C4×C16×D53 | 2 |
| #7171 | 53 |