Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14530403 | C2 | semidirect |
| 3. #14528829 | C2 | semidirect |
| 4. #14526770 | C2 | semidirect |
| 5. #14526769 | C2 | semidirect |
| 6. #14526768 | C2 | semidirect |
| 7. C17×#1339 | C2 | semidirect |
| 8. C2×D8×D17 | C4 | semidirect |
| 12. #11763063 | C4 | semidirect |
| 14. #11763059 | C4 | semidirect |
| 18. #11762844 | C4 | semidirect |
| 21. #11762591 | C22 | semidirect |
| 23. #11762566 | C22 | semidirect |
| 25. C17×#349 | C22 | semidirect |
| 26. C17×H(3,ℤ/4) | C22 | semidirect |
| 167. #1339 | D17 | semidirect |
| 207. #349 | C2×D17 | semidirect |
| 209. H(3,ℤ/4) | C2×D17 | semidirect |
| 258. C17 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538430 | 2 |
| #14530403 | 2 |
| #14528829 | 2 |
| #14526770 | 2 |
| #14526769 | 2 |
| #14526768 | 2 |
| C17×#1339 | 2 |
| #11868 | 17 |