Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
222 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 85 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. C16×Dic34 | C2 | semidirect |
| 3. #14526853 | C2 | semidirect |
| 4. #14526762 | C2 | semidirect |
| 6. #14526703 | C2 | semidirect |
| 81. Dic34 | M32 | semidirect |
| 149. C17 | #12056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic34 | 2 |
| C8×#63229 | 2 |
| #14526853 | 2 |
| #14526762 | 2 |
| D4⋊#63214 | 2 |
| #14526703 | 2 |
| C17×#2169 | 2 |
| #12056 | 17 |