Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22582872 | C2 | semidirect |
| 2. #22582872 | C2 | semidirect |
| 3. #22582865 | C2 | semidirect |
| 4. #22582863 | C2 | semidirect |
| 5. #22582862 | C2 | semidirect |
| 6. #22582861 | C2 | semidirect |
| 7. #22582858 | C2 | semidirect |
| 8. #22582856 | C2 | semidirect |
| 10. C4×C22⋊D281 | C2 | semidirect |
| 11. #22582839 | C2 | semidirect |
| 12. #22582838 | C2 | semidirect |
| 13. #22582835 | C2 | semidirect |
| 14. C2×C22⋊Dic281 | C2 | semidirect |
| 15. C2×C22⋊C4×C281 | C2 | semidirect |
| 16. C2×Dic562 | C22 | semidirect |
| 22. C2×C4×D281 | C22 | semidirect |
| 23. C4⋊Dic281 | C22 | semidirect |
| 24. C4⋊Dic281 | C22 | semidirect |
| 25. C4⋊Dic281 | C22 | semidirect |
| 26. #17985117 | C22 | semidirect |
| 27. #17985117 | C22 | semidirect |
| 28. #17985117 | C22 | semidirect |
| 29. #17985117 | C22 | semidirect |
| 30. #17985117 | C22 | semidirect |
| 38. #17985115 | C22 | semidirect |
| 39. #17985115 | C22 | semidirect |
| 40. #17985115 | C22 | semidirect |
| 41. C4×Dic281 | C22 | semidirect |
| 42. C4×Dic281 | C22 | semidirect |
| 43. C4×Dic281 | C22 | semidirect |
| 110. C281 | #551 | semidirect |
| 126. C2×C22⋊C4 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582872 | 2 |
| #22582865 | 2 |
| #22582863 | 2 |
| #22582862 | 2 |
| #22582861 | 2 |
| #22582858 | 2 |
| #22582856 | 2 |
| #22582848 | 2 |
| C4×C22⋊D281 | 2 |
| #22582839 | 2 |
| #22582838 | 2 |
| #22582835 | 2 |
| C2×C22⋊Dic281 | 2 |
| C2×C22⋊C4×C281 | 2 |
| #551 | 281 |