Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#11762647 | C2 | semidirect |
| 2. C22×#10587465 | C2 | semidirect |
| 3. #14530875 | C2 | semidirect |
| 4. #14526985 | C2 | semidirect |
| 5. #14526964 | C2 | semidirect |
| 6. #14526962 | C2 | semidirect |
| 39. #10587465 | D4 | semidirect |
| 90. C22×C17 | SD64 | semidirect |
| 135. C17 | #13696 | semidirect |
| 178. C22 | #11762647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762647 | 2 |
| C22×#10587465 | 2 |
| #14530875 | 2 |
| #14526985 | 2 |
| #14526964 | 2 |
| #14526962 | 2 |
| C17×#2215 | 2 |
| #13696 | 17 |