Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14528828 | C2 | semidirect |
| 4. #14526905 | C2 | semidirect |
| 5. C17×#1391 | C2 | semidirect |
| 6. C2×#10587593 | C4 | semidirect |
| 12. #11762832 | C4 | semidirect |
| 14. #11762775 | C4 | semidirect |
| 15. C2×#10587486 | C4 | semidirect |
| 129. #1391 | D17 | semidirect |
| 198. C17 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537499 | 2 |
| #14530447 | 2 |
| #14528828 | 2 |
| #14526905 | 2 |
| C17×#1391 | 2 |
| #12808 | 17 |