Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×D1096 | C2 | semidirect |
| 3. #22577972 | C2 | semidirect |
| 4. #22577877 | C2 | semidirect |
| 5. #22577619 | C2 | semidirect |
| 6. #22577599 | C2 | semidirect |
| 7. #22577409 | C2 | semidirect |
| 8. #22577400 | C2 | semidirect |
| 9. #424×C137 | C2 | semidirect |
| 14. C2×#14555499 | C22 | semidirect |
| 17. C2×D1096 | C22 | semidirect |
| 18. #17984085 | C22 | semidirect |
| 19. #17984076 | C22 | semidirect |
| 22. C4×D548 | C22 | semidirect |
| 26. #17984013 | C22 | semidirect |
| 27. #17984010 | C22 | semidirect |
| 28. #17984010 | C22 | semidirect |
| 32. C4⋊C8×C137 | C22 | semidirect |
| 44. C2×D548 | D4 | semidirect |
| 121. C137 | #3041 | semidirect |
| 129. #424 | D137 | semidirect |
| 151. C4⋊C8 | 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×D1096 | 2 |
| #22577972 | 2 |
| #22577877 | 2 |
| #22577619 | 2 |
| #22577599 | 2 |
| #22577409 | 2 |
| #22577400 | 2 |
| #424×C137 | 2 |
| #3041 | 137 |