Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2302 conjugacy classes of subgroups; only the 832 normal subgroups are shown.
This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 832 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 |
|---|---|---|
| 8. #11763745 | C4 | semidirect |
| 10. C42×#595 | C4 | semidirect |
| 12. #11762655 | C4 | semidirect |
| 13. #11762654 | C4 | semidirect |
| 15. C17×#376 | C4 | semidirect |
| 50. C4×#595 | C42 | semidirect |
| 51. C42×C17 | C42 | semidirect |
| 52. C4×Dic17 | C42 | semidirect |
| 53. C4×Dic17 | C42 | semidirect |
| 85. #595 | #376 | direct (N × H) |
| 97. #376 | #595 | direct (N × H) |
| 122. C17 | C4×#376 | semidirect |
| 143. C42 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763745 | 2 |
| C2×C42×#595 | 2 |
| #95×#595 | 2 |
| D17×#376 | 2 |
| C4×#376 | 17 |