Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
614 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×#10587498 | C2 | semidirect |
| 2. C2×#11763192 | C2 | semidirect |
| 3. C2×#11762614 | C2 | semidirect |
| 4. C2×#11762610 | C2 | semidirect |
| 5. #14529651 | C2 | semidirect |
| 6. #14526861 | C2 | semidirect |
| 273. C17 | #13326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587498 | 2 |
| C2×#11763192 | 2 |
| C2×#11762614 | 2 |
| C2×#11762610 | 2 |
| #14529651 | 2 |
| #14526861 | 2 |
| C22×C17×D16 | 2 |
| #13326 | 17 |