Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578114 | C2 | semidirect |
| 3. #22577751 | C2 | semidirect |
| 4. #22577723 | C2 | semidirect |
| 5. #22577633 | C2 | semidirect |
| 6. #22577604 | C2 | semidirect |
| 7. #22577555 | C2 | semidirect |
| 8. C4×#14555498 | C2 | semidirect |
| 9. #22577468 | C2 | semidirect |
| 10. #102×D137 | C2 | semidirect |
| 11. #476×C137 | C2 | semidirect |
| 14. C2×#14555499 | C22 | semidirect |
| 16. C2×C8×D137 | C22 | semidirect |
| 19. #17984068 | C22 | semidirect |
| 24. C4×Dic274 | C22 | semidirect |
| 27. C4⋊C4×D137 | C22 | semidirect |
| 28. #17984019 | C22 | semidirect |
| 29. #17984011 | C22 | semidirect |
| 30. #17984010 | C22 | semidirect |
| 32. #17984008 | C22 | semidirect |
| 33. #17984008 | C22 | semidirect |
| 34. #17984000 | C22 | semidirect |
| 35. C4×#11764040 | C22 | semidirect |
| 36. C4⋊Q8×C137 | C22 | semidirect |
| 38. #106×C137 | C22 | semidirect |
| 39. C4⋊C8×C137 | C22 | semidirect |
| 89. D548 | SD16 | semidirect |
| 136. C137 | #3295 | semidirect |
| 142. #476 | D137 | semidirect |
| 154. C4⋊Q8 | C2×D137 | semidirect |
| 168. #106 | C2×D137 | semidirect |
| 169. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578114 | 2 |
| D4×D548 | 2 |
| #22577751 | 2 |
| #22577723 | 2 |
| #22577633 | 2 |
| #22577604 | 2 |
| #22577555 | 2 |
| C4×#14555498 | 2 |
| #22577468 | 2 |
| #102×D137 | 2 |
| #476×C137 | 2 |
| #3295 | 137 |