Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
340 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #14543931 | C2 | direct (N × H) |
| 11. C2×#10587556 | C4 | semidirect |
| 15. #11763164 | C4 | semidirect |
| 19. C2×C4×C8×C17 | C4 | semidirect |
| 36. #10587556 | C2×C4 | semidirect |
| 42. C4×C8×C17 | C2×C4 | semidirect |
| 144. C2×C4×C8 | #595 | semidirect |
| 151. C2×C17 | #1414 | semidirect |
| 181. C4×C8 | C2×#595 | semidirect |
| 182. C17 | C2×#1414 | semidirect |
| 269. C2 | #14543931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763718 | 2 |
| C2×#11763716 | 2 |
| #14543931 | 2 |
| C2×#11763164 | 2 |
| C2×#1414 | 17 |