Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14544362 | C2 | semidirect |
| 4. #14544361 | C2 | semidirect |
| 5. #14543611 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11762557 | C4 | semidirect |
| 26. #11762557 | C4 | semidirect |
| 27. #11762553 | C4 | semidirect |
| 28. C17×#331 | C4 | semidirect |
| 185. #331 | #595 | semidirect |
| 227. C17 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545665 | 2 |
| #14544918 | 2 |
| #14544362 | 2 |
| #14544361 | 2 |
| #14543611 | 2 |
| #14527443 | 2 |
| #8935 | 17 |