Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 61. C16×C17 | Q16 | semidirect |
| 137. C17 | #12459 | semidirect |
| 157. C16 | Dic68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531066 | 2 |
| C16×Dic34 | 2 |
| #14528189 | 2 |
| #14528179 | 2 |
| #14526843 | 2 |
| #14526840 | 2 |
| C17×#1372 | 2 |
| #12459 | 17 |