Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #14534427 | C2 | semidirect |
| 4. #14526678 | C2 | semidirect |
| 5. #14526649 | C2 | semidirect |
| 6. #14526640 | C2 | semidirect |
| 30. C17×C4⋊Q8 | Q8 | semidirect |
| 31. C17×#127 | Q8 | semidirect |
| 211. C4⋊Q8 | Dic34 | semidirect |
| 212. #127 | Dic34 | semidirect |
| 248. C17 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14534427 | 2 |
| #14527331 | 2 |
| #14527292 | 2 |
| #14526678 | 2 |
| #14526649 | 2 |
| #14526640 | 2 |
| C17×#1980 | 2 |
| #10378 | 17 |