Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#17984116 | C2 | semidirect |
| 2. C22×#14555495 | C2 | semidirect |
| 3. #22577970 | C2 | semidirect |
| 4. #22577877 | C2 | semidirect |
| 5. #22577617 | C2 | semidirect |
| 6. #22577597 | C2 | semidirect |
| 7. #22577431 | C2 | semidirect |
| 8. #22577397 | C2 | semidirect |
| 9. #418×C137 | C2 | semidirect |
| 13. C2×#14555499 | C22 | semidirect |
| 14. C2×D1096 | C22 | semidirect |
| 18. #17984084 | C22 | semidirect |
| 19. #17984075 | C22 | semidirect |
| 23. #17984050 | C22 | semidirect |
| 26. #17984017 | C22 | semidirect |
| 27. #17984011 | C22 | semidirect |
| 28. #17984008 | C22 | semidirect |
| 32. #102×C137 | C22 | semidirect |
| 39. C2×D548 | D4 | semidirect |
| 121. C137 | #3041 | semidirect |
| 130. #418 | D137 | semidirect |
| 154. #102 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| C22×#14555495 | 2 |
| #22577970 | 2 |
| #22577877 | 2 |
| #22577617 | 2 |
| #22577597 | 2 |
| #22577431 | 2 |
| #22577397 | 2 |
| #418×C137 | 2 |
| #3041 | 137 |