Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 1. Q16×Dic34 | C2 | semidirect |
| 5. #14526843 | C2 | semidirect |
| 6. #14526764 | C2 | semidirect |
| 7. C17×#1332 | C2 | semidirect |
| 61. Q16×C17 | SD16 | semidirect |
| 104. Dic34 | SD32 | semidirect |
| 116. #1332 | D17 | semidirect |
| 180. C17 | #12354 | semidirect |
| 189. Q16 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic34 | 2 |
| #14531008 | 2 |
| #14530824 | 2 |
| #14528145 | 2 |
| #14526843 | 2 |
| #14526764 | 2 |
| C17×#1332 | 2 |
| #12354 | 17 |