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. #11763715 | C4 | direct (N × H) |
| 11. #11762716 | C4 | semidirect |
| 14. #11762674 | C4 | semidirect |
| 16. C42×Dic17 | C4 | semidirect |
| 17. C2×C4×Q8×C17 | C4 | semidirect |
| 51. C2×Q8×C17 | C42 | semidirect |
| 84. C4×Dic17 | C42 | semidirect |
| 144. C4×C17 | #354 | semidirect |
| 149. C2×C4×Q8 | #595 | semidirect |
| 195. C17 | C4×#354 | semidirect |
| 200. C2×Q8 | C4×#595 | semidirect |
| 292. C4 | #11763715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763715 | 2 |
| C4×#10587539 | 2 |
| #14543879 | 2 |
| C4×#10587633 | 2 |
| C4×#354 | 17 |