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×#17984116 | C2 | semidirect |
| 2. C2×#17984110 | C2 | semidirect |
| 3. #22577972 | C2 | semidirect |
| 4. #22577883 | C2 | semidirect |
| 5. #22577626 | C2 | semidirect |
| 6. #22577619 | C2 | semidirect |
| 7. #22577604 | C2 | semidirect |
| 8. #22577599 | C2 | semidirect |
| 9. #22577405 | C2 | semidirect |
| 10. C2×#17984010 | C2 | semidirect |
| 11. #424×C137 | C2 | semidirect |
| 17. C2×Dic548 | C22 | semidirect |
| 19. C2×#14555499 | C22 | semidirect |
| 20. C2×#14555499 | C22 | semidirect |
| 22. C2×D1096 | C22 | semidirect |
| 28. C4×Dic274 | C22 | semidirect |
| 29. C4×D548 | C22 | semidirect |
| 34. #17984013 | C22 | semidirect |
| 37. #17984010 | C22 | semidirect |
| 41. C4⋊C8×C137 | C22 | semidirect |
| 42. C4⋊C8×C137 | C22 | semidirect |
| 47. #14555510 | D4 | semidirect |
| 154. C137 | #3045 | semidirect |
| 164. #424 | D137 | semidirect |
| 192. C4⋊C8 | C2×D137 | semidirect |
| 193. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| C2×#17984110 | 2 |
| #22577972 | 2 |
| #22577883 | 2 |
| #22577626 | 2 |
| #22577619 | 2 |
| #22577604 | 2 |
| #22577599 | 2 |
| #22577405 | 2 |
| C2×#17984010 | 2 |
| #424×C137 | 2 |
| #3045 | 137 |