Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22578110 | C2 | semidirect |
| 3. #22577750 | C2 | semidirect |
| 4. #22577722 | C2 | semidirect |
| 5. #22577694 | C2 | semidirect |
| 6. #22577632 | C2 | semidirect |
| 7. #22577604 | C2 | semidirect |
| 8. #22577556 | C2 | semidirect |
| 9. C4×#14555499 | C2 | semidirect |
| 10. C2×#17984010 | C2 | semidirect |
| 11. C8×D4×C137 | C2 | semidirect |
| 15. C2×#14555499 | C22 | semidirect |
| 16. #17984088 | C22 | semidirect |
| 19. #17984067 | C22 | semidirect |
| 24. C4×Dic274 | C22 | semidirect |
| 27. C2×C4⋊Dic137 | C22 | semidirect |
| 28. #17984020 | C22 | semidirect |
| 29. #17984020 | C22 | semidirect |
| 30. #17984013 | C22 | semidirect |
| 33. #17984010 | C22 | semidirect |
| 34. #17984010 | C22 | semidirect |
| 35. #17984010 | C22 | semidirect |
| 36. C22×C8×C137 | C22 | semidirect |
| 38. C4⋊C8×C137 | C22 | semidirect |
| 39. C22⋊C8×C137 | C22 | semidirect |
| 40. C4×C8×C137 | C22 | semidirect |
| 100. D4×C137 | SD16 | semidirect |
| 136. C137 | #3295 | semidirect |
| 147. C8×D4 | D137 | semidirect |
| 153. C22×C8 | C2×D137 | semidirect |
| 169. C4⋊C8 | C2×D137 | semidirect |
| 176. C22⋊C8 | C2×D137 | semidirect |
| 177. C4×C8 | C2×D137 | semidirect |
| 231. D4 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578110 | 2 |
| D4×D548 | 2 |
| #22577750 | 2 |
| #22577722 | 2 |
| #22577694 | 2 |
| #22577632 | 2 |
| #22577604 | 2 |
| #22577556 | 2 |
| C4×#14555499 | 2 |
| C2×#17984010 | 2 |
| C8×D4×C137 | 2 |
| #3295 | 137 |