Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923800 | C2 | semidirect |
| 2. C2×D4×Dic167 | C2 | semidirect |
| 3. #24923600 | C2 | semidirect |
| 4. #24923580 | C2 | semidirect |
| 5. #24923571 | C2 | semidirect |
| 6. #24923482 | C2 | semidirect |
| 7. #24923420 | C2 | semidirect |
| 8. #24923381 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 15. #19128823 | C22 | semidirect |
| 16. #19128819 | C22 | semidirect |
| 19. #19128797 | C22 | semidirect |
| 25. D4×Dic167 | C22 | semidirect |
| 30. #19128765 | C22 | semidirect |
| 31. #19128764 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 33. #19128757 | C22 | semidirect |
| 35. #19128753 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923800 | 2 |
| C2×D4×Dic167 | 2 |
| #24923600 | 2 |
| #24923580 | 2 |
| #24923571 | 2 |
| #24923482 | 2 |
| #24923420 | 2 |
| #24923381 | 2 |
| #24923366 | 2 |
| #24923323 | 2 |
| #447×C167 | 2 |
| #3114 | 167 |