Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22577754 | C2 | semidirect |
| 4. #22577739 | C2 | semidirect |
| 5. #22577699 | C2 | semidirect |
| 6. #22577644 | C2 | semidirect |
| 7. #22577614 | C2 | semidirect |
| 8. #22577561 | C2 | semidirect |
| 9. C4×Dic548 | C2 | semidirect |
| 10. C2×#17984013 | C2 | semidirect |
| 93. D4×C137 | Q16 | semidirect |
| 122. C137 | #3299 | semidirect |
| 208. D4 | Dic548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578110 | 2 |
| D4×Dic274 | 2 |
| #22577754 | 2 |
| #22577739 | 2 |
| #22577699 | 2 |
| #22577644 | 2 |
| #22577614 | 2 |
| #22577561 | 2 |
| C4×Dic548 | 2 |
| C2×#17984013 | 2 |
| C8×D4×C137 | 2 |
| #3299 | 137 |