Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#17984868 | C2 | semidirect |
| 2. #22581499 | C2 | semidirect |
| 3. C2×D4×Dic139 | C2 | semidirect |
| 4. #22581170 | C2 | semidirect |
| 5. #22581166 | C2 | semidirect |
| 6. #22581156 | C2 | semidirect |
| 7. #22581146 | C2 | semidirect |
| 8. #22580976 | C2 | semidirect |
| 9. #22580955 | C2 | semidirect |
| 10. #22580954 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 18. #17984840 | C22 | semidirect |
| 19. #17984838 | C22 | semidirect |
| 20. #17984831 | C22 | semidirect |
| 21. #17984829 | C22 | semidirect |
| 33. Dic139⋊C8 | C22 | semidirect |
| 34. Dic139⋊C8 | C22 | semidirect |
| 35. #17984767 | C22 | semidirect |
| 36. #17984766 | C22 | semidirect |
| 37. #17984764 | C22 | semidirect |
| 38. #17984763 | C22 | semidirect |
| 84. C2×D4×C139 | D4 | semidirect |
| 158. Dic139 | AGL(1,ℤ/8) | semidirect |
| 166. C139 | #3036 | semidirect |
| 169. C2×AGL(1,ℤ/8) | D139 | semidirect |
| 226. C2×D4 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984868 | 2 |
| #22581499 | 2 |
| C2×D4×Dic139 | 2 |
| #22581170 | 2 |
| #22581166 | 2 |
| #22581156 | 2 |
| #22581146 | 2 |
| #22580976 | 2 |
| #22580955 | 2 |
| #22580954 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3036 | 139 |