Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 52. Dic274 | Q16 | semidirect |
| 59. Q8×C137 | Q16 | semidirect |
| 82. C137 | #1633 | semidirect |
| 137. Q8 | Dic548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic274 | 2 |
| #22577783 | 2 |
| #22577699 | 2 |
| #22577698 | 2 |
| #22577151 | 2 |
| #22577135 | 2 |
| Q8⋊C8×C137 | 2 |
| #1633 | 137 |