Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
416 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 416 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. #14543913 | C2 | direct (N × H) |
| 16. #11763201 | C4 | semidirect |
| 18. C2×#10587474 | C4 | semidirect |
| 19. C2×C17×C4⋊Q8 | C4 | semidirect |
| 27. C17×C4⋊Q8 | C2×C4 | semidirect |
| 50. #10587474 | C2×C4 | semidirect |
| 153. C2×C4⋊Q8 | #595 | semidirect |
| 168. C2×C17 | #1407 | semidirect |
| 187. C4⋊Q8 | C2×#595 | semidirect |
| 203. C17 | C2×#1407 | semidirect |
| 303. C2 | #14543913 | 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 |
| #14543913 | 2 |
| C2×#11763201 | 2 |
| C2×#1407 | 17 |