Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 17. C17×#499 | C4 | semidirect |
| 18. C17×#498 | C4 | semidirect |
| 51. #10587483 | Q8 | semidirect |
| 53. C2×#63214 | Q8 | semidirect |
| 131. #499 | Dic17 | semidirect |
| 132. #498 | Dic17 | semidirect |
| 177. C17 | #13291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530389 | 2 |
| #14528908 | 2 |
| #14526900 | 2 |
| #14526891 | 2 |
| #14526885 | 2 |
| #14526882 | 2 |
| C17×#3163 | 2 |
| #13291 | 17 |