Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #14528401 | C2 | semidirect |
| 4. #14526853 | C2 | semidirect |
| 5. #14526839 | C2 | semidirect |
| 6. #14526838 | C2 | semidirect |
| 49. D8×C17 | Q16 | semidirect |
| 150. C17 | #12445 | semidirect |
| 158. D8 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530921 | 2 |
| #14528401 | 2 |
| D8×#3622 | 2 |
| #14526853 | 2 |
| #14526839 | 2 |
| #14526838 | 2 |
| C17×#2224 | 2 |
| #12445 | 17 |