Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19128865 | C2 | semidirect |
| 2. C2×#19128860 | C2 | semidirect |
| 3. C2×#19128854 | C2 | semidirect |
| 4. C22×#14581939 | C2 | semidirect |
| 5. #24923845 | C2 | semidirect |
| 6. #24923838 | C2 | semidirect |
| 7. #24923663 | C2 | semidirect |
| 8. #24923658 | C2 | semidirect |
| 9. #24923653 | C2 | semidirect |
| 10. #24923642 | C2 | semidirect |
| 11. #405×C167 | C2 | semidirect |
| 19. C2×Dic668 | C22 | semidirect |
| 20. C2×Dic668 | C22 | semidirect |
| 25. C2×#14581939 | C22 | semidirect |
| 26. C2×#14581939 | C22 | semidirect |
| 27. C2×#14581939 | C22 | semidirect |
| 29. C2×D1336 | C22 | semidirect |
| 30. #19128832 | C22 | semidirect |
| 33. #19128820 | C22 | semidirect |
| 41. #97×C167 | C22 | semidirect |
| 42. C4×C8×C167 | C22 | semidirect |
| 80. M16×C167 | D4 | semidirect |
| 81. C2×C8×C167 | D4 | semidirect |
| 148. C167 | #3154 | semidirect |
| 160. #405 | D167 | semidirect |
| 190. #97 | C2×D167 | semidirect |
| 191. C4×C8 | C2×D167 | semidirect |
| 226. M16 | D668 | semidirect |
| 227. C2×C8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128865 | 2 |
| C2×#19128860 | 2 |
| C2×#19128854 | 2 |
| C22×#14581939 | 2 |
| #24923845 | 2 |
| #24923838 | 2 |
| #24923663 | 2 |
| #24923658 | 2 |
| #24923653 | 2 |
| #24923642 | 2 |
| #405×C167 | 2 |
| #3154 | 167 |