Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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×#11762648 | C2 | semidirect |
| 2. #14530875 | C2 | semidirect |
| 4. #14526986 | C2 | semidirect |
| 5. #14526966 | C2 | semidirect |
| 6. #14526963 | C2 | semidirect |
| 7. C22×C17×C32 | C2 | semidirect |
| 39. C17×C32 | D4 | semidirect |
| 79. C22×C32 | D17 | semidirect |
| 87. C22×C17 | SD64 | semidirect |
| 134. C32 | C22⋊D17 | semidirect |
| 135. C17 | #13696 | semidirect |
| 178. C22 | #11762648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762648 | 2 |
| #14530875 | 2 |
| #14530870 | 2 |
| #14526986 | 2 |
| #14526966 | 2 |
| #14526963 | 2 |
| C22×C17×C32 | 2 |
| #13696 | 17 |