Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22578127 | C2 | semidirect |
| 3. #22577751 | C2 | semidirect |
| 4. #22577729 | C2 | semidirect |
| 5. #22577633 | C2 | semidirect |
| 6. #22577604 | C2 | semidirect |
| 7. #22577568 | C2 | semidirect |
| 8. C4×#14555500 | C2 | semidirect |
| 9. #22577468 | C2 | semidirect |
| 10. #22577398 | C2 | semidirect |
| 11. #475×C137 | C2 | semidirect |
| 127. C137 | #3304 | semidirect |
| 133. #475 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578127 | 2 |
| #22578075 | 2 |
| #22577751 | 2 |
| #22577729 | 2 |
| #22577633 | 2 |
| #22577604 | 2 |
| #22577568 | 2 |
| C4×#14555500 | 2 |
| #22577468 | 2 |
| #22577398 | 2 |
| #475×C137 | 2 |
| #3304 | 137 |