Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22581607 | C2 | semidirect |
| 2. #22581299 | C2 | semidirect |
| 3. #22581264 | C2 | semidirect |
| 4. #22581233 | C2 | semidirect |
| 5. #22581187 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581087 | C2 | semidirect |
| 8. C4×#14555770 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. C2×#17984763 | C2 | semidirect |
| 11. D42×C139 | C2 | semidirect |
| 14. C2×#14555770 | C22 | semidirect |
| 15. C22×C139⋊C8 | C22 | semidirect |
| 16. #17984842 | C22 | semidirect |
| 19. #17984816 | C22 | semidirect |
| 20. C4×D556 | C22 | semidirect |
| 21. C2×C4⋊Dic139 | C22 | semidirect |
| 22. #17984775 | C22 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. C4⋊(C139⋊C8) | C22 | semidirect |
| 27. #17984763 | C22 | semidirect |
| 28. #17984763 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 30. #17984762 | C22 | semidirect |
| 31. C22⋊(C139⋊C8) | C22 | semidirect |
| 32. C4×C139⋊C8 | C22 | semidirect |
| 103. D4×C139 | D8 | semidirect |
| 104. D4×C139 | #41 | semidirect |
| 142. C139 | #3294 | semidirect |
| 145. D42 | D139 | semidirect |
| 239. D4 | #14555770 | semidirect |
| 240. D4 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581607 | 2 |
| #22581299 | 2 |
| #22581264 | 2 |
| #22581233 | 2 |
| #22581187 | 2 |
| #22581145 | 2 |
| #22581087 | 2 |
| C4×#14555770 | 2 |
| D4×C139⋊C8 | 2 |
| C2×#17984763 | 2 |
| D42×C139 | 2 |
| #3294 | 139 |