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×#17984113 | C2 | semidirect |
| 2. C22×#14555495 | C2 | semidirect |
| 3. #22577877 | C2 | semidirect |
| 4. #22577615 | C2 | semidirect |
| 5. #22577595 | C2 | semidirect |
| 6. #22577430 | C2 | semidirect |
| 7. #22577408 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 9. #535×C137 | C2 | semidirect |
| 12. C2×#14555497 | C22 | semidirect |
| 15. C2×#14555495 | C22 | semidirect |
| 18. C4×D548 | C22 | semidirect |
| 22. C4⋊#11764040 | C22 | semidirect |
| 23. #17984012 | C22 | semidirect |
| 24. #17984009 | C22 | semidirect |
| 25. #17984009 | C22 | semidirect |
| 28. #127×C137 | C22 | semidirect |
| 29. #124×C137 | C22 | semidirect |
| 36. C2×D548 | D4 | semidirect |
| 121. C137 | #3041 | semidirect |
| 125. #535 | D137 | semidirect |
| 142. #127 | C2×D137 | semidirect |
| 143. #124 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984113 | 2 |
| C22×#14555495 | 2 |
| #22577877 | 2 |
| #22577615 | 2 |
| #22577595 | 2 |
| #22577430 | 2 |
| #22577408 | 2 |
| #22577399 | 2 |
| #535×C137 | 2 |
| #3041 | 137 |