Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
450 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 80 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. #14544242 | C2 | semidirect |
| 4. #14544178 | C2 | semidirect |
| 5. #14543671 | C2 | semidirect |
| 6. #14543650 | C2 | semidirect |
| 25. #11763096 | C4 | semidirect |
| 26. #11763019 | C4 | semidirect |
| 27. #11763015 | C4 | semidirect |
| 32. C17×#477 | C4 | semidirect |
| 200. #477 | #595 | semidirect |
| 276. C17 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545628 | 2 |
| #14544548 | 2 |
| #14544242 | 2 |
| #14544178 | 2 |
| #14543671 | 2 |
| #14543650 | 2 |
| #14538949 | 2 |
| #9160 | 17 |