Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#17984113 | C2 | semidirect |
| 2. C2×#17984094 | C2 | semidirect |
| 3. #22577981 | C2 | semidirect |
| 4. #22577972 | C2 | semidirect |
| 5. #22577655 | C2 | semidirect |
| 6. #22577652 | C2 | semidirect |
| 7. #22577638 | C2 | semidirect |
| 8. #22577635 | C2 | semidirect |
| 9. #22577446 | C2 | semidirect |
| 10. C2×#17984010 | C2 | semidirect |
| 11. #416×C137 | C2 | semidirect |
| 19. C2×#14555493 | C22 | semidirect |
| 20. C2×C8×D137 | C22 | semidirect |
| 24. #17984064 | C22 | semidirect |
| 29. #17984059 | C22 | semidirect |
| 32. #17984021 | C22 | semidirect |
| 33. #17984019 | C22 | semidirect |
| 39. #103×C137 | C22 | semidirect |
| 40. #103×C137 | C22 | semidirect |
| 41. #102×C137 | C22 | semidirect |
| 42. #102×C137 | C22 | semidirect |
| 60. #14555494 | D4 | semidirect |
| 151. C137 | #3062 | semidirect |
| 162. #416 | D137 | semidirect |
| 189. #103 | C2×D137 | semidirect |
| 190. #103 | C2×D137 | semidirect |
| 193. #102 | C2×D137 | semidirect |
| 194. #102 | 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×#17984094 | 2 |
| #22577981 | 2 |
| #22577972 | 2 |
| #22577655 | 2 |
| #22577652 | 2 |
| #22577638 | 2 |
| #22577635 | 2 |
| #22577446 | 2 |
| C2×#17984010 | 2 |
| #416×C137 | 2 |
| #3062 | 137 |