Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
556 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14540172 | C2 | semidirect |
| 3. #14539158 | C2 | semidirect |
| 4. #14527375 | C2 | semidirect |
| 5. #14527206 | C2 | semidirect |
| 6. #14526673 | C2 | semidirect |
| 7. C17×#1965 | C2 | semidirect |
| 169. #1965 | D17 | semidirect |
| 268. C17 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540172 | 2 |
| #14539702 | 2 |
| #14539158 | 2 |
| #14527375 | 2 |
| #14527206 | 2 |
| #14526673 | 2 |
| C17×#1965 | 2 |
| #10112 | 17 |