Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
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. #14545131 | C2 | semidirect |
| 4. #14543846 | C2 | semidirect |
| 17. C2×#10587469 | C4 | semidirect |
| 19. C22×#63214 | C4 | semidirect |
| 20. C2×C16×D17 | C4 | semidirect |
| 22. C2×C17×M32 | C4 | semidirect |
| 136. C2×M32 | #595 | semidirect |
| 185. C17 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545131 | 2 |
| #14544668 | 2 |
| #14544666 | 2 |
| #14543846 | 2 |
| C2×#11763227 | 2 |
| #12832 | 17 |