Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128851 | C2 | semidirect |
| 2. #24923913 | C2 | semidirect |
| 3. #24923652 | C2 | semidirect |
| 4. #24923510 | C2 | semidirect |
| 5. #24923502 | C2 | semidirect |
| 6. #24923482 | C2 | semidirect |
| 7. #24923420 | C2 | semidirect |
| 8. #24923411 | C2 | semidirect |
| 9. D8×Dic167 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. C22×D8×C167 | C2 | semidirect |
| 12. C2×#14581949 | C22 | semidirect |
| 14. C2×Dic668 | C22 | semidirect |
| 15. C2×#14581938 | C22 | semidirect |
| 16. C2×#14581938 | C22 | semidirect |
| 17. C2×C8×D167 | C22 | semidirect |
| 18. #19128819 | C22 | semidirect |
| 22. #19128803 | C22 | semidirect |
| 24. D4×Dic167 | C22 | semidirect |
| 27. #19128766 | C22 | semidirect |
| 28. Dic167⋊C8 | C22 | semidirect |
| 29. #19128757 | C22 | semidirect |
| 30. #19128753 | C22 | semidirect |
| 31. #19128753 | C22 | semidirect |
| 33. (C2×D167)⋊C8 | C22 | semidirect |
| 34. C8×Dic167 | C22 | semidirect |
| 76. D8×C167 | D4 | semidirect |
| 123. C22×C167 | #135 | semidirect |
| 143. C167 | #3280 | semidirect |
| 146. C22×D8 | D167 | semidirect |
| 206. D8 | C22⋊D167 | semidirect |
| 270. C22 | #19128851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| #24923913 | 2 |
| #24923652 | 2 |
| #24923510 | 2 |
| #24923502 | 2 |
| #24923482 | 2 |
| #24923420 | 2 |
| #24923411 | 2 |
| D8×Dic167 | 2 |
| C8×C22⋊D167 | 2 |
| C22×D8×C167 | 2 |
| #3280 | 167 |