Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#17984095 | C2 | semidirect |
| 3. #22577967 | C2 | semidirect |
| 4. #22577654 | C2 | semidirect |
| 5. #22577651 | C2 | semidirect |
| 6. #22577637 | C2 | semidirect |
| 7. #22577634 | C2 | semidirect |
| 8. #22577443 | C2 | semidirect |
| 9. #22577399 | C2 | semidirect |
| 10. C2×#17984008 | C2 | semidirect |
| 11. #537×C137 | C2 | semidirect |
| 18. C2×#14555494 | C22 | semidirect |
| 20. C22×#11764040 | C22 | semidirect |
| 27. #17984021 | C22 | semidirect |
| 28. #17984019 | C22 | semidirect |
| 29. #17984012 | C22 | semidirect |
| 30. #17984012 | C22 | semidirect |
| 31. #17984009 | C22 | semidirect |
| 32. #17984009 | C22 | semidirect |
| 38. C22⋊Q8×C137 | C22 | semidirect |
| 41. #121×C137 | C22 | semidirect |
| 53. #14555494 | D4 | semidirect |
| 151. C137 | #3062 | semidirect |
| 155. #537 | D137 | semidirect |
| 178. C22⋊Q8 | C2×D137 | semidirect |
| 183. #121 | 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 |
| C2×#17984095 | 2 |
| #22577967 | 2 |
| #22577654 | 2 |
| #22577651 | 2 |
| #22577637 | 2 |
| #22577634 | 2 |
| #22577443 | 2 |
| #22577399 | 2 |
| C2×#17984008 | 2 |
| #537×C137 | 2 |
| #3062 | 137 |