Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984116 | C2 | semidirect |
| 2. #22577981 | C2 | semidirect |
| 3. #22577967 | C2 | semidirect |
| 4. #22577656 | C2 | semidirect |
| 5. #22577649 | C2 | semidirect |
| 6. #22577639 | C2 | semidirect |
| 7. #22577632 | C2 | semidirect |
| 8. #22577445 | C2 | semidirect |
| 9. #22577400 | C2 | semidirect |
| 10. C2×#17984010 | C2 | semidirect |
| 11. C2×#131×C137 | C2 | semidirect |
| 19. #17984067 | C22 | semidirect |
| 23. #17984062 | C22 | semidirect |
| 29. #17984022 | C22 | semidirect |
| 30. #17984020 | C22 | semidirect |
| 31. #17984013 | C22 | semidirect |
| 32. #17984013 | C22 | semidirect |
| 35. #17984010 | C22 | semidirect |
| 36. #17984010 | C22 | semidirect |
| 40. C2×M16×C137 | C22 | semidirect |
| 42. C22×C8×C137 | C22 | semidirect |
| 79. M16×C137 | D4 | semidirect |
| 151. C137 | #3062 | semidirect |
| 154. C2×#131 | D137 | semidirect |
| 172. C2×M16 | C2×D137 | semidirect |
| 174. C22×C8 | C2×D137 | semidirect |
| 220. M16 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| #22577981 | 2 |
| #22577967 | 2 |
| #22577656 | 2 |
| #22577649 | 2 |
| #22577639 | 2 |
| #22577632 | 2 |
| #22577445 | 2 |
| #22577400 | 2 |
| C2×#17984010 | 2 |
| C2×#131×C137 | 2 |
| #3062 | 137 |