Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
308 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #11763734 | C4 | semidirect |
| 15. #11763733 | C4 | semidirect |
| 16. #11763696 | C4 | semidirect |
| 17. C16×#595 | C4 | semidirect |
| 23. #11762633 | C4 | semidirect |
| 24. #11762632 | C4 | semidirect |
| 25. #11762631 | C4 | semidirect |
| 26. C17×#365 | C4 | semidirect |
| 156. #365 | #595 | semidirect |
| 198. C17 | #12668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545132 | 2 |
| M32×#595 | 2 |
| #14544589 | 2 |
| #14544587 | 2 |
| #14543853 | 2 |
| #14543851 | 2 |
| #14530555 | 2 |
| #12668 | 17 |