Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
364 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14539308 | C2 | semidirect |
| 3. #14526898 | C2 | semidirect |
| 4. #14526864 | C2 | semidirect |
| 20. C2×Q16×C17 | Q8 | semidirect |
| 22. C2×D8×C17 | Q8 | semidirect |
| 138. C2×Q16 | Dic34 | semidirect |
| 140. C2×D8 | Dic34 | semidirect |
| 161. C17 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539308 | 2 |
| #14530520 | 2 |
| #14526898 | 2 |
| #14526864 | 2 |
| C17×#1975 | 2 |
| #13373 | 17 |