Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#19128858 | C2 | semidirect |
| 2. C2×#19128839 | C2 | semidirect |
| 3. #24923847 | C2 | semidirect |
| 4. #24923520 | C2 | semidirect |
| 5. #24923513 | C2 | semidirect |
| 6. #24923503 | C2 | semidirect |
| 7. #24923496 | C2 | semidirect |
| 8. #24923312 | C2 | semidirect |
| 9. #24923263 | C2 | semidirect |
| 10. C2×#19128753 | C2 | semidirect |
| 11. #535×C167 | C2 | semidirect |
| 18. C2×#14581934 | C22 | semidirect |
| 20. C22×C167⋊C8 | C22 | semidirect |
| 21. #19128811 | C22 | semidirect |
| 23. #19128806 | C22 | semidirect |
| 27. #19128765 | C22 | semidirect |
| 28. #19128763 | C22 | semidirect |
| 29. #19128755 | C22 | semidirect |
| 30. #19128755 | C22 | semidirect |
| 33. #19128752 | C22 | semidirect |
| 34. #19128752 | C22 | semidirect |
| 54. #14581934 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 156. #535 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| C2×#19128839 | 2 |
| #24923847 | 2 |
| #24923520 | 2 |
| #24923513 | 2 |
| #24923503 | 2 |
| #24923496 | 2 |
| #24923312 | 2 |
| #24923263 | 2 |
| C2×#19128753 | 2 |
| #535×C167 | 2 |
| #3062 | 167 |