Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
458 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 1. #14540000 | C2 | semidirect |
| 4. #14527256 | C2 | semidirect |
| 5. #14527206 | C2 | semidirect |
| 7. C17×#1291 | C2 | semidirect |
| 167. #1291 | D17 | semidirect |
| 266. C17 | #10125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540000 | 2 |
| #14539789 | 2 |
| #14539171 | 2 |
| #14527256 | 2 |
| #14527206 | 2 |
| #14527137 | 2 |
| C17×#1291 | 2 |
| #10125 | 17 |