Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 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. C8×C22⋊#595 | C2 | semidirect |
| 3. #14543666 | C2 | semidirect |
| 4. #14543664 | C2 | semidirect |
| 10. #11763663 | C4 | semidirect |
| 11. #11763660 | C4 | semidirect |
| 16. #11762837 | C4 | semidirect |
| 17. #11762776 | C4 | semidirect |
| 19. #11762764 | C4 | semidirect |
| 20. C2×C17×#131 | C4 | semidirect |
| 144. C2×#131 | #595 | semidirect |
| 194. C17 | #8238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C22⋊#595 | 2 |
| #14544159 | 2 |
| #14543666 | 2 |
| #14543664 | 2 |
| #14537476 | 2 |
| #8238 | 17 |