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. #22581766 | C2 | semidirect |
| 2. #22581762 | C2 | semidirect |
| 3. #22581758 | C2 | semidirect |
| 4. #22581338 | C2 | semidirect |
| 5. #22581224 | C2 | semidirect |
| 6. #22581219 | C2 | semidirect |
| 7. #22581129 | C2 | semidirect |
| 8. #22581128 | C2 | semidirect |
| 9. #22581069 | C2 | semidirect |
| 10. #22581068 | C2 | semidirect |
| 11. #473×C139 | C2 | semidirect |
| 12. #17984890 | C22 | semidirect |
| 16. #17984873 | C22 | semidirect |
| 19. #17984870 | C22 | semidirect |
| 27. C2×#14555772 | C22 | semidirect |
| 31. #17984850 | C22 | semidirect |
| 32. #17984848 | C22 | semidirect |
| 33. #17984831 | C22 | semidirect |
| 34. #17984777 | C22 | semidirect |
| 36. #17984768 | C22 | semidirect |
| 37. #17984768 | C22 | semidirect |
| 38. #17984758 | C22 | semidirect |
| 39. C8×Dic139 | C22 | semidirect |
| 41. C2×Q16×C139 | C22 | semidirect |
| 43. #108×C139 | C22 | semidirect |
| 44. #101×C139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 155. #473 | D139 | semidirect |
| 178. C2×Q16 | C2×D139 | semidirect |
| 188. #108 | C2×D139 | semidirect |
| 192. #101 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581766 | 2 |
| #22581762 | 2 |
| #22581758 | 2 |
| #22581338 | 2 |
| #22581224 | 2 |
| #22581219 | 2 |
| #22581129 | 2 |
| #22581128 | 2 |
| #22581069 | 2 |
| #22581068 | 2 |
| #473×C139 | 2 |
| #3290 | 139 |