Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 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 |
|---|---|---|
| 2. C2×#17984119 | C2 | semidirect |
| 3. #22577977 | C2 | semidirect |
| 4. #22577562 | C2 | semidirect |
| 5. #22577552 | C2 | semidirect |
| 6. #22577408 | C2 | semidirect |
| 7. #22577400 | C2 | semidirect |
| 8. #22577369 | C2 | semidirect |
| 9. C22×SD16×C137 | C2 | semidirect |
| 20. C2×#14555500 | C22 | semidirect |
| 21. C2×#14555497 | C22 | semidirect |
| 22. C2×#14555494 | C22 | semidirect |
| 26. #17984064 | C22 | semidirect |
| 27. #17984047 | C22 | semidirect |
| 28. #17984013 | C22 | semidirect |
| 29. #17984010 | C22 | semidirect |
| 30. #17984009 | C22 | semidirect |
| 31. #17984000 | C22 | semidirect |
| 32. C22×Q8×C137 | C22 | semidirect |
| 35. C2×SD16×C137 | C22 | semidirect |
| 36. C22×C8×C137 | C22 | semidirect |
| 146. C137 | #3009 | semidirect |
| 150. C22×SD16 | D137 | semidirect |
| 163. C22×Q8 | C2×D137 | semidirect |
| 172. C2×SD16 | C2×D137 | semidirect |
| 174. C22×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984133 | 2 |
| C2×#17984119 | 2 |
| #22577977 | 2 |
| #22577562 | 2 |
| #22577552 | 2 |
| #22577408 | 2 |
| #22577400 | 2 |
| #22577369 | 2 |
| C22×SD16×C137 | 2 |
| #3009 | 137 |