Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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. #14544276 | C2 | semidirect |
| 3. #14544207 | C2 | semidirect |
| 5. #14543651 | C2 | semidirect |
| 6. #14543644 | C2 | semidirect |
| 20. #11763212 | C4 | semidirect |
| 21. #11763183 | C4 | semidirect |
| 22. #11763156 | C4 | semidirect |
| 26. C17×#487 | C4 | semidirect |
| 166. #487 | #595 | semidirect |
| 226. C17 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545671 | 2 |
| #14544276 | 2 |
| #14544207 | 2 |
| #14544205 | 2 |
| #14543651 | 2 |
| #14543644 | 2 |
| #14539505 | 2 |
| #9415 | 17 |