Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
494 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 3. #14544999 | C2 | semidirect |
| 4. #14543827 | C2 | semidirect |
| 15. #11763706 | C4 | semidirect |
| 16. #11763705 | C4 | semidirect |
| 21. #11762591 | C4 | semidirect |
| 22. #11762590 | C4 | semidirect |
| 23. C17×#349 | C4 | semidirect |
| 46. #10587538 | C2×C4 | semidirect |
| 55. C17×M32 | C2×C4 | semidirect |
| 56. #10587483 | C2×C4 | semidirect |
| 182. #349 | #595 | semidirect |
| 217. M32 | C2×#595 | semidirect |
| 226. C17 | #12607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#595 | 2 |
| #14545018 | 2 |
| #14544999 | 2 |
| #14543827 | 2 |
| D17×#349 | 2 |
| #12607 | 17 |