Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14539914 | C2 | semidirect |
| 2. #14539711 | C2 | semidirect |
| 4. #14529757 | C2 | semidirect |
| 5. #14527345 | C2 | semidirect |
| 6. #14527345 | C2 | semidirect |
| 7. C17×#1281 | C2 | semidirect |
| 105. C2×C8×C17 | SD16 | semidirect |
| 174. #1281 | D17 | semidirect |
| 272. C17 | #10221 | semidirect |
| 306. C2×C8 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539914 | 2 |
| #14539711 | 2 |
| #14539230 | 2 |
| #14529757 | 2 |
| #14527345 | 2 |
| C17×#1281 | 2 |
| #10221 | 17 |