Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
568 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 42. C17×C4⋊Q8 | C8 | semidirect |
| 43. #10587630 | C8 | semidirect |
| 49. #10587555 | C8 | semidirect |
| 156. C4×C17 | Q8⋊C8 | semidirect |
| 160. Dic17 | Q8⋊C8 | semidirect |
| 192. C4⋊Q8 | #3633 | semidirect |
| 216. C17 | #9673 | semidirect |
| 320. C4 | Q8⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#3633 | 2 |
| C2×Q8⋊#3633 | 2 |
| C4⋊Q8×#595 | 2 |
| #9673 | 17 |