Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
668 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#10587543 | C2 | semidirect |
| 2. C2×#11763663 | C2 | semidirect |
| 4. #14543960 | C2 | semidirect |
| 17. #11762716 | C4 | semidirect |
| 18. #11762712 | C4 | semidirect |
| 23. #11762675 | C4 | semidirect |
| 24. C2×C17×#124 | C4 | semidirect |
| 217. C2×#124 | #595 | semidirect |
| 284. C17 | #9681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587543 | 2 |
| C2×#11763663 | 2 |
| C2×#11763660 | 2 |
| #14543960 | 2 |
| #14537080 | 2 |
| #9681 | 17 |