Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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. #22581660 | C2 | semidirect |
| 2. #22581299 | C2 | semidirect |
| 3. #22581269 | C2 | semidirect |
| 4. #22581243 | C2 | semidirect |
| 5. #22581180 | C2 | semidirect |
| 6. #22581150 | C2 | semidirect |
| 7. #22581104 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. C2×#17984763 | C2 | semidirect |
| 13. C2×#14555773 | C22 | semidirect |
| 14. C22×C139⋊C8 | C22 | semidirect |
| 15. #17984842 | C22 | semidirect |
| 17. #17984821 | C22 | semidirect |
| 19. C4×Dic278 | C22 | semidirect |
| 21. C2×C4⋊Dic139 | C22 | semidirect |
| 22. #17984773 | C22 | semidirect |
| 23. #17984773 | C22 | semidirect |
| 24. C4⋊(C139⋊C8) | C22 | semidirect |
| 25. #17984765 | C22 | semidirect |
| 28. #17984763 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 30. #17984763 | C22 | semidirect |
| 31. C22⋊(C139⋊C8) | C22 | semidirect |
| 32. C4×C139⋊C8 | C22 | semidirect |
| 100. D4×C139 | SD16 | semidirect |
| 136. C139 | #3295 | semidirect |
| 230. D4 | #14555773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581660 | 2 |
| #22581299 | 2 |
| #22581269 | 2 |
| #22581243 | 2 |
| #22581180 | 2 |
| #22581150 | 2 |
| #22581104 | 2 |
| C4×#14555773 | 2 |
| D4×C139⋊C8 | 2 |
| C2×#17984763 | 2 |
| D42×C139 | 2 |
| #3295 | 139 |