Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128878 | C2 | semidirect |
| 2. C2×#19128857 | C2 | semidirect |
| 3. C22×D1336 | C2 | semidirect |
| 4. #24923838 | C2 | semidirect |
| 5. #24923417 | C2 | semidirect |
| 6. #24923404 | C2 | semidirect |
| 7. #24923273 | C2 | semidirect |
| 8. #24923235 | C2 | semidirect |
| 9. #416×C167 | C2 | semidirect |
| 12. C2×#14581951 | C22 | semidirect |
| 17. C22×D668 | C22 | semidirect |
| 19. C2×D4×D167 | C22 | semidirect |
| 21. C2×#14581937 | C22 | semidirect |
| 23. C2×D1336 | C22 | semidirect |
| 24. C2×#14581935 | C22 | semidirect |
| 25. C2×#14581934 | C22 | semidirect |
| 28. #19128807 | C22 | semidirect |
| 30. #19128752 | C22 | semidirect |
| 31. (C2×D167)⋊C8 | C22 | semidirect |
| 33. C22×C8×C167 | C22 | semidirect |
| 34. #117×C167 | C22 | semidirect |
| 35. #103×C167 | C22 | semidirect |
| 36. #102×C167 | C22 | semidirect |
| 55. C2×D668 | D4 | semidirect |
| 72. #41×C167 | D4 | semidirect |
| 151. C167 | #3008 | semidirect |
| 160. #416 | D167 | semidirect |
| 179. C22×C8 | C2×D167 | semidirect |
| 184. #117 | C2×D167 | semidirect |
| 185. #103 | C2×D167 | semidirect |
| 187. #102 | C2×D167 | semidirect |
| 198. #41 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128878 | 2 |
| C2×#19128857 | 2 |
| C22×D1336 | 2 |
| #24923838 | 2 |
| #24923417 | 2 |
| #24923404 | 2 |
| #24923273 | 2 |
| #24923235 | 2 |
| #416×C167 | 2 |
| #3008 | 167 |