Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 15. #11763669 | C4 | semidirect |
| 18. #11762558 | C4 | semidirect |
| 19. #11762557 | C4 | semidirect |
| 20. C17×#333 | C4 | semidirect |
| 126. #595 | #333 | direct (N × H) |
| 149. #333 | #595 | direct (N × H) |
| 180. C17 | C4×#333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×#595 | 2 |
| C4⋊C8×#595 | 2 |
| D17⋊#333 | 2 |
| #14543663 | 2 |
| D17×#333 | 2 |
| C4×#333 | 17 |