Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3250 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14545356 | C2 | semidirect |
| 3. C4×#10587680 | C2 | semidirect |
| 4. #14545350 | C2 | semidirect |
| 5. C4×D17⋊M16 | C2 | semidirect |
| 7. #11763889 | C4 | direct (N × H) |
| 10. #11763774 | C22 | semidirect |
| 11. C4×#63243 | C22 | semidirect |
| 12. C4×#63243 | C22 | semidirect |
| 15. #11763768 | C22 | semidirect |
| 16. C4×#63242 | C22 | semidirect |
| 37. #10587680 | C2×C4 | semidirect |
| 38. D17⋊M16 | C2×C4 | semidirect |
| 90. #63243 | C22×C4 | semidirect |
| 91. #63242 | C22×C4 | semidirect |
| 152. C4×C17 | #568 | semidirect |
| 156. Dic17 | #568 | semidirect |
| 222. C17 | C4×#568 | semidirect |
| 307. C4 | #11763889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763889 | 2 |
| #14545356 | 2 |
| C4×#10587680 | 2 |
| #14545350 | 2 |
| C4×D17⋊M16 | 2 |
| C2×C4×#63256 | 2 |
| C4×#568 | 17 |