Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 3. #14539336 | C2 | semidirect |
| 4. #14527256 | C2 | semidirect |
| 6. #14527141 | C2 | semidirect |
| 7. C17×#1291 | C2 | semidirect |
| 165. #1291 | D17 | semidirect |
| 263. C17 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539976 | 2 |
| #14539797 | 2 |
| #14539336 | 2 |
| #14527256 | 2 |
| #14527202 | 2 |
| #14527141 | 2 |
| C17×#1291 | 2 |
| #10126 | 17 |