Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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 |
|---|---|---|
| 1. C2×#17984888 | C2 | semidirect |
| 2. C22×#14555770 | C2 | semidirect |
| 3. #22581520 | C2 | semidirect |
| 4. #22581097 | C2 | semidirect |
| 5. #22581085 | C2 | semidirect |
| 6. #22580959 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580921 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 12. C2×#14555786 | C22 | semidirect |
| 18. C2×D4×D139 | C22 | semidirect |
| 20. C2×#14555770 | C22 | semidirect |
| 21. C22×C139⋊C8 | C22 | semidirect |
| 24. #17984813 | C22 | semidirect |
| 26. #17984801 | C22 | semidirect |
| 27. #17984766 | C22 | semidirect |
| 28. #17984764 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 30. (C2×D139)⋊C8 | C22 | semidirect |
| 32. C22×D4×C139 | C22 | semidirect |
| 34. C2×SD16×C139 | C22 | semidirect |
| 35. C2×D8×C139 | C22 | semidirect |
| 36. C2×M16×C139 | C22 | semidirect |
| 50. C2×D556 | D4 | semidirect |
| 69. #41×C139 | D4 | semidirect |
| 151. C139 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D139 | semidirect |
| 172. C22×D4 | C2×D139 | semidirect |
| 174. C2×SD16 | C2×D139 | semidirect |
| 177. C2×D8 | C2×D139 | semidirect |
| 178. C2×M16 | C2×D139 | semidirect |
| 198. #41 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984888 | 2 |
| C22×#14555770 | 2 |
| #22581520 | 2 |
| #22581097 | 2 |
| #22581085 | 2 |
| #22580959 | 2 |
| #22580949 | 2 |
| #22580921 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3008 | 139 |