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×#17984096 | C2 | semidirect |
| 2. #22577981 | C2 | semidirect |
| 3. #22577970 | C2 | semidirect |
| 4. #22577653 | C2 | semidirect |
| 5. #22577646 | C2 | semidirect |
| 6. #22577636 | C2 | semidirect |
| 7. #22577629 | C2 | semidirect |
| 8. #22577445 | C2 | semidirect |
| 9. #22577399 | C2 | semidirect |
| 10. C2×#17984009 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C137 | C2 | semidirect |
| 14. C2×#14555493 | C22 | semidirect |
| 16. C2×C8×D137 | C22 | semidirect |
| 20. #17984064 | C22 | semidirect |
| 25. #17984059 | C22 | semidirect |
| 29. #17984022 | C22 | semidirect |
| 30. #17984020 | C22 | semidirect |
| 31. #17984012 | C22 | semidirect |
| 32. #17984012 | C22 | semidirect |
| 35. #17984009 | C22 | semidirect |
| 36. #17984009 | C22 | semidirect |
| 83. M16×C137 | D4 | semidirect |
| 151. C137 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | 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×#17984096 | 2 |
| #22577981 | 2 |
| #22577970 | 2 |
| #22577653 | 2 |
| #22577646 | 2 |
| #22577636 | 2 |
| #22577629 | 2 |
| #22577445 | 2 |
| #22577399 | 2 |
| C2×#17984009 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #3062 | 137 |