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×#19128877 | C2 | semidirect |
| 2. C2×#19128860 | C2 | semidirect |
| 3. C22×#14581935 | C2 | semidirect |
| 4. #24923838 | C2 | semidirect |
| 5. #24923415 | C2 | semidirect |
| 6. #24923404 | C2 | semidirect |
| 7. #24923263 | C2 | semidirect |
| 8. #24923237 | C2 | semidirect |
| 9. #418×C167 | C2 | semidirect |
| 15. C2×#14581949 | C22 | semidirect |
| 16. C22×D668 | C22 | semidirect |
| 19. C2×D4×D167 | C22 | semidirect |
| 21. C2×#14581939 | C22 | semidirect |
| 22. C2×D1336 | C22 | semidirect |
| 24. C2×#14581935 | C22 | semidirect |
| 25. C22×C167⋊C8 | C22 | semidirect |
| 28. #19128807 | C22 | semidirect |
| 30. #19128755 | C22 | semidirect |
| 31. #19128752 | C22 | semidirect |
| 32. (C2×D167)⋊C8 | C22 | semidirect |
| 34. C2×M16×C167 | C22 | semidirect |
| 35. #117×C167 | C22 | semidirect |
| 36. #102×C167 | C22 | semidirect |
| 42. #14581950 | D4 | semidirect |
| 75. C2×D4×C167 | D4 | semidirect |
| 151. C167 | #3008 | semidirect |
| 159. #418 | D167 | semidirect |
| 178. C2×M16 | C2×D167 | semidirect |
| 184. #117 | C2×D167 | semidirect |
| 187. #102 | C2×D167 | semidirect |
| 218. C2×D4 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128877 | 2 |
| C2×#19128860 | 2 |
| C22×#14581935 | 2 |
| #24923838 | 2 |
| #24923415 | 2 |
| #24923404 | 2 |
| #24923263 | 2 |
| #24923237 | 2 |
| #418×C167 | 2 |
| #3008 | 167 |