Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #14527335 | C2 | semidirect |
| 5. #14527231 | C2 | semidirect |
| 6. #14526650 | C2 | semidirect |
| 7. C17×#3113 | C2 | semidirect |
| 172. #3113 | D17 | semidirect |
| 277. C17 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539173 | 2 |
| #14534644 | 2 |
| #14527407 | 2 |
| #14527335 | 2 |
| #14527231 | 2 |
| #14526650 | 2 |
| C17×#3113 | 2 |
| #10024 | 17 |