Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
466 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. #14545009 | C2 | semidirect |
| 2. #14544470 | C2 | semidirect |
| 3. #14543773 | C2 | semidirect |
| 4. #14543770 | C2 | semidirect |
| 12. C2×#10587598 | C4 | semidirect |
| 16. #11763050 | C4 | semidirect |
| 20. #11762846 | C4 | semidirect |
| 22. C17×#466 | C4 | semidirect |
| 180. #466 | #595 | semidirect |
| 232. C17 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545009 | 2 |
| #14544470 | 2 |
| #14543773 | 2 |
| #14543770 | 2 |
| #14538363 | 2 |
| #11703 | 17 |