Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 43. #10587488 | Q8 | semidirect |
| 45. #10587483 | Q8 | semidirect |
| 168. C17 | #13454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530573 | 2 |
| #14529527 | 2 |
| #14526889 | 2 |
| #14526868 | 2 |
| C17×#3162 | 2 |
| #13454 | 17 |