Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 2. #14530998 | C2 | semidirect |
| 3. #14530558 | C2 | semidirect |
| 4. C2×#11762621 | C2 | semidirect |
| 5. #14530405 | C2 | semidirect |
| 6. C17×#2916 | C2 | semidirect |
| 14. #11762633 | C22 | semidirect |
| 16. #11762591 | C22 | semidirect |
| 20. C17×#430 | C22 | semidirect |
| 114. #2916 | D17 | semidirect |
| 140. #430 | C2×D17 | semidirect |
| 182. C17 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538432 | 2 |
| #14530998 | 2 |
| #14530558 | 2 |
| C2×#11762621 | 2 |
| #14530405 | 2 |
| C17×#2916 | 2 |
| #33657 | 17 |