Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
316 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #14531059 | C2 | semidirect |
| 4. #14528179 | C2 | semidirect |
| 5. #14526840 | C2 | semidirect |
| 6. #14526764 | C2 | semidirect |
| 62. D8×C17 | Q16 | semidirect |
| 178. C17 | #12404 | semidirect |
| 190. D8 | Dic68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic34 | 2 |
| #14531059 | 2 |
| #14530921 | 2 |
| #14528179 | 2 |
| #14526840 | 2 |
| #14526764 | 2 |
| C17×#1331 | 2 |
| #12404 | 17 |