Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
322 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
| 4. #14528154 | C2 | semidirect |
| 5. #14526838 | C2 | semidirect |
| 7. C17×Q8⋊C16 | C2 | semidirect |
| 88. Q8×C17 | SD32 | semidirect |
| 117. Q8⋊C16 | D17 | semidirect |
| 182. C17 | #12356 | semidirect |
| 222. Q8 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D136 | 2 |
| #14531012 | 2 |
| #14530830 | 2 |
| #14528154 | 2 |
| #14526838 | 2 |
| #14526746 | 2 |
| C17×Q8⋊C16 | 2 |
| #12356 | 17 |