Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 38. C17×M32 | Q8 | semidirect |
| 46. #10587490 | Q8 | semidirect |
| 53. C2×#63214 | Q8 | semidirect |
| 171. M32 | Dic34 | semidirect |
| 191. C17 | #13455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539324 | 2 |
| C2×#11762634 | 2 |
| #14529567 | 2 |
| #14526893 | 2 |
| #14526879 | 2 |
| #14526874 | 2 |
| C17×#2159 | 2 |
| #13455 | 17 |