Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. Q16×#3622 | C2 | semidirect |
| 4. #14526847 | C2 | semidirect |
| 5. #14526842 | C2 | semidirect |
| 7. C17×#2227 | C2 | semidirect |
| 51. Q16×C17 | SD16 | semidirect |
| 93. #2227 | D17 | semidirect |
| 153. C17 | #12419 | semidirect |
| 160. Q16 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530824 | 2 |
| #14528377 | 2 |
| Q16×#3622 | 2 |
| #14526847 | 2 |
| #14526842 | 2 |
| #14526831 | 2 |
| C17×#2227 | 2 |
| #12419 | 17 |