Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #14530573 | C2 | semidirect |
| 2. C2×#11762622 | C2 | semidirect |
| 3. C2×#11762610 | C2 | semidirect |
| 4. C2×#11762593 | C2 | semidirect |
| 5. #14528848 | C2 | semidirect |
| 6. #14526879 | C2 | semidirect |
| 63. #10587483 | D4 | semidirect |
| 251. C17 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530573 | 2 |
| C2×#11762622 | 2 |
| C2×#11762610 | 2 |
| C2×#11762593 | 2 |
| #14528848 | 2 |
| #14526879 | 2 |
| C17×#3058 | 2 |
| #13387 | 17 |