Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
298 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 298 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. #14531012 | C2 | semidirect |
| 3. #14530835 | C2 | semidirect |
| 5. #14526841 | C2 | semidirect |
| 6. #14526749 | C2 | semidirect |
| 88. D4×C17 | Q32 | semidirect |
| 180. C17 | #12346 | semidirect |
| 220. D4 | Dic136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541177 | 2 |
| #14531012 | 2 |
| #14530835 | 2 |
| #14528149 | 2 |
| #14526841 | 2 |
| #14526749 | 2 |
| C17×D4⋊C16 | 2 |
| #12346 | 17 |