Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14530049 | C2 | semidirect |
| 4. #14526802 | C2 | semidirect |
| 6. #14526725 | C2 | semidirect |
| 7. C17×#2188 | C2 | semidirect |
| 140. #2188 | D17 | semidirect |
| 223. C17 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540246 | 2 |
| #14530701 | 2 |
| #14530049 | 2 |
| #14526802 | 2 |
| #14526800 | 2 |
| #14526725 | 2 |
| C17×#2188 | 2 |
| #12169 | 17 |