Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984114 | C2 | semidirect |
| 2. C22×#14555495 | C2 | semidirect |
| 3. #22577972 | C2 | semidirect |
| 4. #22577618 | C2 | semidirect |
| 5. #22577598 | C2 | semidirect |
| 6. #22577430 | C2 | semidirect |
| 7. #22577407 | C2 | semidirect |
| 8. #22577397 | C2 | semidirect |
| 9. #518×C137 | C2 | semidirect |
| 13. C2×#14555498 | C22 | semidirect |
| 16. C2×#14555495 | C22 | semidirect |
| 19. #17984085 | C22 | semidirect |
| 20. #17984076 | C22 | semidirect |
| 23. C4⋊#11764040 | C22 | semidirect |
| 24. #17984011 | C22 | semidirect |
| 25. #17984008 | C22 | semidirect |
| 26. #17984008 | C22 | semidirect |
| 29. C4×D4×C137 | C22 | semidirect |
| 56. C2×D4×C137 | D4 | semidirect |
| 121. C137 | #3041 | semidirect |
| 126. #518 | D137 | semidirect |
| 147. C4×D4 | C2×D137 | semidirect |
| 169. C2×D4 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984114 | 2 |
| C22×#14555495 | 2 |
| #22577972 | 2 |
| #22577618 | 2 |
| #22577598 | 2 |
| #22577430 | 2 |
| #22577407 | 2 |
| #22577397 | 2 |
| #518×C137 | 2 |
| #3041 | 137 |