Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923803 | C2 | semidirect |
| 2. C2×C4×D668 | C2 | semidirect |
| 3. #24923600 | C2 | semidirect |
| 4. #24923583 | C2 | semidirect |
| 5. #24923570 | C2 | semidirect |
| 6. #24923485 | C2 | semidirect |
| 7. #24923422 | C2 | semidirect |
| 9. #24923382 | C2 | semidirect |
| 10. #24923371 | C2 | semidirect |
| 11. #432×C167 | C2 | semidirect |
| 17. #19128824 | C22 | semidirect |
| 18. #19128820 | C22 | semidirect |
| 22. C4×Dic334 | C22 | semidirect |
| 27. C4×D668 | C22 | semidirect |
| 32. #19128766 | C22 | semidirect |
| 33. #19128764 | C22 | semidirect |
| 34. #19128757 | C22 | semidirect |
| 37. #19128754 | C22 | semidirect |
| 39. C4⋊C8×C167 | C22 | semidirect |
| 42. #97×C167 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 152. #432 | D167 | semidirect |
| 176. C4⋊C8 | C2×D167 | semidirect |
| 183. #97 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| C2×C4×D668 | 2 |
| #24923600 | 2 |
| #24923583 | 2 |
| #24923570 | 2 |
| #24923485 | 2 |
| #24923422 | 2 |
| #24923405 | 2 |
| #24923382 | 2 |
| #24923371 | 2 |
| #432×C167 | 2 |
| #3114 | 167 |