Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14544542 | C2 | semidirect |
| 4. #14544541 | C2 | semidirect |
| 5. #14543874 | C2 | semidirect |
| 6. #14543871 | C2 | semidirect |
| 9. C22×#63243 | C4 | semidirect |
| 14. #11763815 | C4 | semidirect |
| 18. #11763781 | C4 | semidirect |
| 21. #11763773 | C4 | semidirect |
| 22. #11763711 | C4 | semidirect |
| 23. #11763710 | C4 | semidirect |
| 29. #11762599 | C4 | semidirect |
| 30. #11762597 | C4 | semidirect |
| 31. #11762595 | C4 | semidirect |
| 32. C17×#352 | C4 | semidirect |
| 236. #352 | #595 | semidirect |
| 299. C17 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545505 | 2 |
| #14545038 | 2 |
| #14544542 | 2 |
| #14544541 | 2 |
| #14543874 | 2 |
| #14543871 | 2 |
| #14530424 | 2 |
| #12624 | 17 |