Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #14537652 | C2 | semidirect |
| 4. #14530848 | C2 | semidirect |
| 5. #14530832 | C2 | semidirect |
| 6. #14530542 | C2 | semidirect |
| 7. #14530504 | C2 | semidirect |
| 9. C22×C17×Q32 | C2 | semidirect |
| 156. C22×Q32 | D17 | semidirect |
| 248. C17 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763250 | 2 |
| #14539273 | 2 |
| #14537652 | 2 |
| #14530848 | 2 |
| #14530832 | 2 |
| #14530542 | 2 |
| #14530504 | 2 |
| #14530492 | 2 |
| C22×C17×Q32 | 2 |
| #33588 | 17 |