Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
990 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14545350 | C2 | semidirect |
| 3. #14544484 | C2 | semidirect |
| 4. C2×#11763680 | C2 | semidirect |
| 9. #11763807 | C4 | semidirect |
| 18. #11762715 | C4 | semidirect |
| 19. #11762714 | C4 | semidirect |
| 20. #11762712 | C4 | semidirect |
| 23. C17×#390 | C4 | semidirect |
| 122. #63243 | C22⋊C4 | semidirect |
| 236. #390 | #595 | semidirect |
| 293. C17 | #10959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763807 | 2 |
| #14545350 | 2 |
| #14544484 | 2 |
| C2×#11763680 | 2 |
| #14531271 | 2 |
| #10959 | 17 |