Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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. #22578483 | C2 | semidirect |
| 2. #22578482 | C2 | semidirect |
| 3. C2×#17984176 | C2 | semidirect |
| 4. D137⋊#131 | C2 | semidirect |
| 6. #17984176 | C22 | semidirect |
| 7. #17984176 | C22 | semidirect |
| 8. #17984176 | C22 | semidirect |
| 9. #17984175 | C22 | semidirect |
| 10. #17984175 | C22 | semidirect |
| 11. C2×#14555520 | C22 | semidirect |
| 12. D137⋊M16 | C22 | semidirect |
| 13. C2×#14555518 | C22 | semidirect |
| 58. C137 | #3573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578483 | 2 |
| #22578482 | 2 |
| C2×#17984176 | 2 |
| D137⋊#131 | 2 |
| #22578240 | 2 |
| #3573 | 137 |