Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578202 | C2 | semidirect |
| 2. C2×#17984111 | C2 | semidirect |
| 3. #131×D137 | C2 | semidirect |
| 4. #22577675 | C2 | semidirect |
| 5. #22577674 | C2 | semidirect |
| 6. #22577673 | C2 | semidirect |
| 7. #22577669 | C2 | semidirect |
| 8. #22577668 | C2 | semidirect |
| 9. #108×D137 | C2 | semidirect |
| 10. #22577386 | C2 | semidirect |
| 11. #473×C137 | C2 | semidirect |
| 25. C2×#14555497 | C22 | semidirect |
| 26. C2×D1096 | C22 | semidirect |
| 37. #17984024 | C22 | semidirect |
| 38. #17984023 | C22 | semidirect |
| 39. #17984007 | C22 | semidirect |
| 40. #17984004 | C22 | semidirect |
| 41. #17984004 | C22 | semidirect |
| 43. C2×Q16×C137 | C22 | semidirect |
| 45. #108×C137 | C22 | semidirect |
| 46. #101×C137 | C22 | semidirect |
| 166. C137 | #3067 | semidirect |
| 172. #473 | D137 | semidirect |
| 193. C2×Q16 | C2×D137 | semidirect |
| 209. #108 | C2×D137 | semidirect |
| 211. #101 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578202 | 2 |
| C2×#17984111 | 2 |
| #131×D137 | 2 |
| #22577675 | 2 |
| #22577674 | 2 |
| #22577673 | 2 |
| #22577669 | 2 |
| #22577668 | 2 |
| #108×D137 | 2 |
| #22577386 | 2 |
| #473×C137 | 2 |
| #3067 | 137 |