Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1566 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 440 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 |
|---|---|---|
| 6. #11763754 | C4 | direct (N × H) |
| 12. C42×Dic17 | C4 | semidirect |
| 13. C42×Dic17 | C4 | semidirect |
| 14. C42×Dic17 | C4 | semidirect |
| 15. C43×C17 | C4 | semidirect |
| 56. C42×C17 | C42 | semidirect |
| 63. C4×Dic17 | C42 | semidirect |
| 102. C4×C17 | #383 | semidirect |
| 105. Dic17 | #383 | semidirect |
| 116. C43 | #595 | semidirect |
| 141. C17 | C4×#383 | semidirect |
| 169. C42 | C4×#595 | semidirect |
| 206. C4 | #11763754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763754 | 2 |
| #14543960 | 2 |
| C4×(C2×#595)⋊C4 | 2 |
| C43×D17 | 2 |
| C4×#383 | 17 |