Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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. #16811552 | C4 | semidirect |
| 10. #16811551 | C4 | semidirect |
| 11. #16811550 | C4 | semidirect |
| 12. #16811549 | C4 | semidirect |
| 17. C4×#11719908 | C4 | semidirect |
| 18. C16×Dic53 | C4 | semidirect |
| 19. C16×Dic53 | C4 | semidirect |
| 20. C4×C16×C53 | C4 | semidirect |
| 129. C4×C16 | #6157 | semidirect |
| 131. C53 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| #20291066 | 2 |
| #20290517 | 2 |
| #20289777 | 2 |
| C4×C16×D53 | 2 |
| #12670 | 53 |