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. #24923805 | C2 | semidirect |
| 2. C2×D4×Dic167 | C2 | semidirect |
| 3. #24923597 | C2 | semidirect |
| 4. #24923583 | C2 | semidirect |
| 5. #24923567 | C2 | semidirect |
| 6. #24923486 | C2 | semidirect |
| 8. #24923378 | C2 | semidirect |
| 9. #24923370 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #450×C167 | C2 | semidirect |
| 15. #19128823 | C22 | semidirect |
| 16. #19128821 | C22 | semidirect |
| 19. Q8×Dic167 | C22 | semidirect |
| 24. #19128794 | C22 | semidirect |
| 30. #19128766 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 33. #19128756 | C22 | semidirect |
| 34. #19128754 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 148. #450 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923805 | 2 |
| C2×D4×Dic167 | 2 |
| #24923597 | 2 |
| #24923583 | 2 |
| #24923567 | 2 |
| #24923486 | 2 |
| #24923403 | 2 |
| #24923378 | 2 |
| #24923370 | 2 |
| #24923323 | 2 |
| #450×C167 | 2 |
| #3114 | 167 |