Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. #14530496 | C2 | semidirect |
| 4. C2×#11762590 | C2 | semidirect |
| 5. #14528814 | C2 | semidirect |
| 6. #14526891 | C2 | semidirect |
| 7. C2×C17×#360 | C2 | semidirect |
| 59. C17×M32 | D4 | semidirect |
| 180. C2×#360 | 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 |
|---|---|
| #14538389 | 2 |
| #14530572 | 2 |
| #14530496 | 2 |
| C2×#11762590 | 2 |
| #14528814 | 2 |
| #14526891 | 2 |
| C2×C17×#360 | 2 |
| #13386 | 17 |