Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. #14544969 | C2 | semidirect |
| 4. #14544107 | C2 | semidirect |
| 5. #14543670 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763086 | C4 | semidirect |
| 26. #11763019 | C4 | semidirect |
| 27. #11763015 | C4 | semidirect |
| 32. C17×#475 | C4 | semidirect |
| 211. #475 | #595 | semidirect |
| 287. C17 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545714 | 2 |
| #14544969 | 2 |
| C4×#10587550 | 2 |
| #14544107 | 2 |
| #14543670 | 2 |
| #14543611 | 2 |
| #14538858 | 2 |
| #8971 | 17 |