Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #14530572 | C2 | semidirect |
| 3. C2×#11762620 | C2 | semidirect |
| 4. #14530497 | C2 | semidirect |
| 5. #14528817 | C2 | semidirect |
| 6. #14526890 | C2 | semidirect |
| 7. C2×C17×#349 | C2 | semidirect |
| 61. C17×M32 | D4 | semidirect |
| 182. C2×#349 | D17 | semidirect |
| 268. M32 | C22⋊D17 | semidirect |
| 283. C17 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538393 | 2 |
| #14530572 | 2 |
| C2×#11762620 | 2 |
| #14530497 | 2 |
| #14528817 | 2 |
| #14526890 | 2 |
| C2×C17×#349 | 2 |
| #13386 | 17 |