Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20291062 | C2 | semidirect |
| 4. #20289777 | C2 | semidirect |
| 17. C2×#13133156 | C4 | semidirect |
| 19. C22×#11719908 | C4 | semidirect |
| 20. C2×C16×D53 | C4 | semidirect |
| 22. C2×M32×C53 | C4 | semidirect |
| 141. C2×M32 | #6157 | semidirect |
| 153. C53 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291062 | 2 |
| #20290599 | 2 |
| #20290597 | 2 |
| #20289777 | 2 |
| C2×#16811041 | 2 |
| #12832 | 53 |