Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
388 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14543925 | C2 | semidirect |
| 7. #11763366 | C4 | semidirect |
| 9. #11763174 | C4 | semidirect |
| 13. C4×M16×C17 | C4 | semidirect |
| 25. #10587556 | C2×C4 | semidirect |
| 30. C17×#97 | C2×C4 | semidirect |
| 109. C4×M16 | #595 | semidirect |
| 135. #97 | C2×#595 | semidirect |
| 137. C17 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763714 | 2 |
| #14543925 | 2 |
| #14539159 | 2 |
| #13595 | 17 |