Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581505 | C2 | semidirect |
| 3. #22581289 | C2 | semidirect |
| 4. #22581286 | C2 | semidirect |
| 5. #22581231 | C2 | semidirect |
| 6. #22581156 | C2 | semidirect |
| 8. #22581054 | C2 | semidirect |
| 9. #22581050 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 14. #17984841 | C22 | semidirect |
| 15. #17984840 | C22 | semidirect |
| 19. Q8×Dic139 | C22 | semidirect |
| 21. #17984807 | C22 | semidirect |
| 30. #17984776 | C22 | semidirect |
| 31. #17984775 | C22 | semidirect |
| 32. Dic139⋊C8 | C22 | semidirect |
| 33. #17984767 | C22 | semidirect |
| 34. #17984766 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 136. C139 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581505 | 2 |
| C2×D4×Dic139 | 2 |
| #22581289 | 2 |
| #22581286 | 2 |
| #22581231 | 2 |
| #22581156 | 2 |
| #22581104 | 2 |
| #22581054 | 2 |
| #22581050 | 2 |
| #22581007 | 2 |
| #450×C139 | 2 |
| #3110 | 139 |