Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #14545126 | C2 | semidirect |
| 4. #14544704 | C2 | semidirect |
| 5. #14543857 | C2 | semidirect |
| 6. #14543848 | C2 | semidirect |
| 20. #11762922 | C4 | semidirect |
| 21. #11762920 | C4 | semidirect |
| 22. #11762916 | C4 | semidirect |
| 28. C17×#441 | C4 | semidirect |
| 185. #441 | #595 | semidirect |
| 247. C17 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545126 | 2 |
| #14545106 | 2 |
| #14545100 | 2 |
| #14544704 | 2 |
| #14543857 | 2 |
| #14543848 | 2 |
| #14537664 | 2 |
| #12828 | 17 |