Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×#11763715 | C2 | semidirect |
| 2. C2×#11763665 | C2 | semidirect |
| 3. #14543907 | C2 | direct (N × H) |
| 8. #11763715 | C22 | semidirect |
| 10. #11763665 | C22 | semidirect |
| 15. #11762982 | C4 | semidirect |
| 18. C2×#10587507 | C4 | semidirect |
| 19. C2×C17×2−1+4 | C4 | semidirect |
| 23. C17×2−1+4 | C2×C4 | semidirect |
| 52. #10587507 | C2×C4 | semidirect |
| 175. C2×2−1+4 | #595 | semidirect |
| 193. C2×C17 | #1404 | semidirect |
| 200. 2−1+4 | C2×#595 | semidirect |
| 230. C17 | C2×#1404 | semidirect |
| 353. C2 | #14543907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763715 | 2 |
| C2×#11763665 | 2 |
| #14543907 | 2 |
| C2×#11762982 | 2 |
| C2×#1404 | 17 |