Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 1. Q8×Dic68 | C2 | semidirect |
| 5. #14526841 | C2 | semidirect |
| 6. #14526749 | C2 | semidirect |
| 7. C17×Q8⋊C16 | C2 | semidirect |
| 78. Dic68 | SD16 | semidirect |
| 87. Q8×C17 | SD32 | semidirect |
| 115. Q8⋊C16 | D17 | semidirect |
| 180. C17 | #12354 | semidirect |
| 218. Q8 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic68 | 2 |
| #14531008 | 2 |
| #14530825 | 2 |
| #14528144 | 2 |
| #14526841 | 2 |
| #14526749 | 2 |
| C17×Q8⋊C16 | 2 |
| #12354 | 17 |