Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581770 | C2 | semidirect |
| 2. #22581763 | C2 | semidirect |
| 3. #22581754 | C2 | semidirect |
| 4. #22581336 | C2 | semidirect |
| 5. #22581229 | C2 | semidirect |
| 6. #22581215 | C2 | semidirect |
| 7. #22581133 | C2 | semidirect |
| 8. #22581124 | C2 | semidirect |
| 9. #22581069 | C2 | semidirect |
| 10. #22581068 | C2 | semidirect |
| 11. #472×C139 | C2 | semidirect |
| 12. #17984889 | C22 | semidirect |
| 16. #17984875 | C22 | semidirect |
| 27. C2×Dic556 | C22 | semidirect |
| 28. C2×#14555773 | C22 | semidirect |
| 31. #17984850 | C22 | semidirect |
| 33. #17984829 | C22 | semidirect |
| 34. #17984777 | C22 | semidirect |
| 35. #17984769 | C22 | semidirect |
| 37. #17984768 | C22 | semidirect |
| 38. #17984760 | C22 | semidirect |
| 39. C8×Dic139 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C139 | C22 | semidirect |
| 42. #131×C139 | C22 | semidirect |
| 43. #108×C139 | C22 | semidirect |
| 44. #100×C139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 156. #472 | D139 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D139 | semidirect |
| 185. #131 | C2×D139 | semidirect |
| 188. #108 | C2×D139 | semidirect |
| 193. #100 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581770 | 2 |
| #22581763 | 2 |
| #22581754 | 2 |
| #22581336 | 2 |
| #22581229 | 2 |
| #22581215 | 2 |
| #22581133 | 2 |
| #22581124 | 2 |
| #22581069 | 2 |
| #22581068 | 2 |
| #472×C139 | 2 |
| #3290 | 139 |