Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14540186 | C2 | semidirect |
| 3. #14530068 | C2 | semidirect |
| 4. #14526778 | C2 | semidirect |
| 5. #14526776 | C2 | semidirect |
| 6. #14526734 | C2 | semidirect |
| 7. C17×#2191 | C2 | semidirect |
| 150. #2191 | D17 | semidirect |
| 238. C17 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540186 | 2 |
| #14530730 | 2 |
| #14530068 | 2 |
| #14526778 | 2 |
| #14526776 | 2 |
| #14526734 | 2 |
| C17×#2191 | 2 |
| #12175 | 17 |