Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
412 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 412 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. #14543866 | C2 | semidirect |
| 6. #14543851 | C2 | semidirect |
| 20. #11762922 | C4 | semidirect |
| 21. #11762921 | C4 | semidirect |
| 22. #11762920 | C4 | semidirect |
| 28. C17×#442 | C4 | semidirect |
| 192. #442 | #595 | semidirect |
| 255. C17 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545126 | 2 |
| D17⋊#361 | 2 |
| #14545093 | 2 |
| #14544704 | 2 |
| #14543866 | 2 |
| #14543851 | 2 |
| #14537633 | 2 |
| #12826 | 17 |