Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923915 | C2 | semidirect |
| 3. #24923653 | C2 | semidirect |
| 4. #24923515 | C2 | semidirect |
| 5. #24923485 | C2 | semidirect |
| 6. #24923433 | C2 | semidirect |
| 7. #24923405 | C2 | semidirect |
| 8. C4×D1336 | C2 | semidirect |
| 9. #436×C167 | C2 | semidirect |
| 11. C22×D668 | C22 | semidirect |
| 13. C2×Dic668 | C22 | semidirect |
| 14. C2×#14581939 | C22 | semidirect |
| 15. C2×#14581939 | C22 | semidirect |
| 19. #19128820 | C22 | semidirect |
| 21. #19128811 | C22 | semidirect |
| 25. C4×D668 | C22 | semidirect |
| 27. #19128766 | C22 | semidirect |
| 28. #19128757 | C22 | semidirect |
| 29. #19128754 | C22 | semidirect |
| 30. #19128754 | C22 | semidirect |
| 31. C2×M16×C167 | C22 | semidirect |
| 33. C4⋊C8×C167 | C22 | semidirect |
| 34. C22⋊C8×C167 | C22 | semidirect |
| 35. C4×C8×C167 | C22 | semidirect |
| 54. D1336 | D4 | semidirect |
| 124. C167 | #3273 | semidirect |
| 134. #436 | D167 | semidirect |
| 144. C2×M16 | C2×D167 | semidirect |
| 155. C4⋊C8 | C2×D167 | semidirect |
| 159. C22⋊C8 | C2×D167 | semidirect |
| 160. C4×C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128860 | 2 |
| #24923915 | 2 |
| #24923653 | 2 |
| #24923515 | 2 |
| #24923485 | 2 |
| #24923433 | 2 |
| #24923405 | 2 |
| C4×D1336 | 2 |
| #436×C167 | 2 |
| #3273 | 167 |