Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
650 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11763244 | C2 | semidirect |
| 2. C2×#11763184 | C2 | semidirect |
| 3. C2×#11762623 | C2 | semidirect |
| 4. C2×#11762622 | C2 | semidirect |
| 5. #14529673 | C2 | semidirect |
| 6. #14526865 | C2 | semidirect |
| 7. C2×C17×#509 | C2 | semidirect |
| 39. C2×Q16×C17 | D4 | semidirect |
| 47. C2×D8×C17 | D4 | semidirect |
| 66. C17×M32 | D4 | semidirect |
| 77. #10587483 | D4 | semidirect |
| 180. C2×#509 | D17 | semidirect |
| 244. C2×Q16 | C22⋊D17 | semidirect |
| 261. C2×D8 | C22⋊D17 | semidirect |
| 275. M32 | C22⋊D17 | semidirect |
| 284. C17 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763244 | 2 |
| C2×#11763184 | 2 |
| C2×#11762623 | 2 |
| C2×#11762622 | 2 |
| #14529673 | 2 |
| #14526865 | 2 |
| C2×C17×#509 | 2 |
| #13331 | 17 |