Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 2. #14531956 | C2 | semidirect |
| 3. C2×#11762605 | C2 | semidirect |
| 4. #14528743 | C2 | semidirect |
| 5. #14526911 | C2 | semidirect |
| 6. #14526910 | C2 | semidirect |
| 7. C17×#1793 | C2 | semidirect |
| 11. #11762982 | C4 | semidirect |
| 34. C17×2−1+4 | C2×C4 | semidirect |
| 78. #10587507 | C2×C4 | semidirect |
| 235. #1793 | D17 | semidirect |
| 298. 2−1+4 | C4×D17 | semidirect |
| 349. C17 | #13055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762982 | 2 |
| #14531956 | 2 |
| C2×#11762605 | 2 |
| #14528743 | 2 |
| #14526911 | 2 |
| #14526910 | 2 |
| C17×#1793 | 2 |
| #13055 | 17 |