Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22578369 | C2 | semidirect |
| 4. #22578362 | C2 | semidirect |
| 5. #22578278 | C2 | semidirect |
| 6. #22578274 | C2 | semidirect |
| 8. #17984176 | C4 | semidirect |
| 10. #17984175 | C4 | semidirect |
| 17. #17984151 | C4 | semidirect |
| 18. #17984150 | C4 | semidirect |
| 25. #17984016 | C4 | semidirect |
| 26. #17984015 | C4 | semidirect |
| 27. #17984014 | C4 | semidirect |
| 28. #104×C137 | C4 | semidirect |
| 120. C137 | #1765 | semidirect |
| 144. #104 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#131 | 2 |
| #22578393 | 2 |
| #22578369 | 2 |
| #22578362 | 2 |
| #22578278 | 2 |
| #22578274 | 2 |
| #104×D137 | 2 |
| #1765 | 137 |