Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. #14544207 | C2 | semidirect |
| 4. #14544107 | C2 | semidirect |
| 5. #14543645 | C2 | semidirect |
| 6. #14543640 | C2 | semidirect |
| 26. #11763219 | C4 | semidirect |
| 27. #11763171 | C4 | semidirect |
| 28. #11763169 | C4 | semidirect |
| 34. C17×#501 | C4 | semidirect |
| 195. #501 | #595 | semidirect |
| 277. C17 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545608 | 2 |
| #14544227 | 2 |
| #14544207 | 2 |
| #14544107 | 2 |
| #14543645 | 2 |
| #14543640 | 2 |
| #14540027 | 2 |
| #9369 | 17 |