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×#19128860 | C2 | semidirect |
| 2. C2×#19128840 | C2 | semidirect |
| 3. #24923850 | C2 | semidirect |
| 4. #24923838 | C2 | semidirect |
| 5. #24923523 | C2 | semidirect |
| 6. #24923516 | C2 | semidirect |
| 7. #24923506 | C2 | semidirect |
| 8. #24923499 | C2 | semidirect |
| 9. #24923263 | C2 | semidirect |
| 10. C2×#19128752 | C2 | semidirect |
| 11. #428×C167 | C2 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 21. C2×C8×D167 | C22 | semidirect |
| 25. #19128812 | C22 | semidirect |
| 29. #19128807 | C22 | semidirect |
| 32. #19128755 | C22 | semidirect |
| 33. #19128755 | C22 | semidirect |
| 36. #19128752 | C22 | semidirect |
| 37. #19128752 | C22 | semidirect |
| 41. #107×C167 | C22 | semidirect |
| 42. #106×C167 | C22 | semidirect |
| 77. M16×C167 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 161. #428 | D167 | semidirect |
| 187. #107 | C2×D167 | semidirect |
| 188. #106 | C2×D167 | semidirect |
| 220. M16 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128860 | 2 |
| C2×#19128840 | 2 |
| #24923850 | 2 |
| #24923838 | 2 |
| #24923523 | 2 |
| #24923516 | 2 |
| #24923506 | 2 |
| #24923499 | 2 |
| #24923263 | 2 |
| C2×#19128752 | 2 |
| #428×C167 | 2 |
| #3062 | 167 |