Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
588 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14545925 | C2 | semidirect |
| 2. #14545924 | C2 | semidirect |
| 3. #14545784 | C2 | semidirect |
| 4. #14545783 | C2 | semidirect |
| 49. C17×#121 | C8 | semidirect |
| 51. #10587624 | C8 | semidirect |
| 52. #10587616 | C8 | semidirect |
| 53. #10587581 | C8 | semidirect |
| 276. #121 | #3633 | semidirect |
| 300. C17 | #7599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545925 | 2 |
| #14545924 | 2 |
| #14545784 | 2 |
| #14545783 | 2 |
| #121×#595 | 2 |
| #7599 | 17 |