Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 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×#11762644 | C2 | semidirect |
| 2. C22×#10587465 | C2 | semidirect |
| 3. #14530870 | C2 | semidirect |
| 4. #14526983 | C2 | semidirect |
| 5. #14526962 | C2 | semidirect |
| 6. #14526961 | C2 | semidirect |
| 7. C17×#2215 | C2 | semidirect |
| 39. #10587465 | D4 | semidirect |
| 82. #2215 | D17 | semidirect |
| 91. C22×C17 | D32 | semidirect |
| 139. C17 | #13694 | semidirect |
| 186. C22 | #11762644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762644 | 2 |
| C22×#10587465 | 2 |
| #14530870 | 2 |
| #14526983 | 2 |
| #14526962 | 2 |
| #14526961 | 2 |
| C17×#2215 | 2 |
| #13694 | 17 |