Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
584 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 584 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 |
|---|---|---|
| 7. #11763716 | C4 | direct (N × H) |
| 10. C2×C4×Dic34 | C4 | semidirect |
| 12. #11762715 | C4 | semidirect |
| 15. #11762675 | C4 | semidirect |
| 17. C43×C17 | C4 | semidirect |
| 66. C2×Dic34 | C42 | semidirect |
| 76. C42×C17 | C42 | semidirect |
| 144. C4×C17 | #354 | semidirect |
| 158. C43 | #595 | semidirect |
| 195. C17 | C4×#354 | semidirect |
| 234. C42 | C4×#595 | semidirect |
| 292. C4 | #11763716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763716 | 2 |
| C4×#10587539 | 2 |
| #14543878 | 2 |
| C4×#10587561 | 2 |
| C4×#354 | 17 |