Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128857 | C2 | semidirect |
| 2. C2×#19128839 | C2 | semidirect |
| 3. #24923833 | C2 | semidirect |
| 4. #24923520 | C2 | semidirect |
| 5. #24923517 | C2 | semidirect |
| 6. #24923503 | C2 | semidirect |
| 7. #24923500 | C2 | semidirect |
| 8. #24923309 | C2 | semidirect |
| 9. #24923265 | C2 | semidirect |
| 10. C2×#19128752 | C2 | semidirect |
| 11. #537×C167 | C2 | semidirect |
| 18. C2×#14581934 | C22 | semidirect |
| 20. C22×C167⋊C8 | C22 | semidirect |
| 27. #19128765 | C22 | semidirect |
| 28. #19128763 | C22 | semidirect |
| 29. #19128756 | C22 | semidirect |
| 30. #19128756 | C22 | semidirect |
| 31. #19128753 | C22 | semidirect |
| 32. #19128753 | C22 | semidirect |
| 38. C22⋊Q8×C167 | C22 | semidirect |
| 41. #121×C167 | C22 | semidirect |
| 53. #14581934 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 155. #537 | D167 | semidirect |
| 178. C22⋊Q8 | C2×D167 | semidirect |
| 183. #121 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128857 | 2 |
| C2×#19128839 | 2 |
| #24923833 | 2 |
| #24923520 | 2 |
| #24923517 | 2 |
| #24923503 | 2 |
| #24923500 | 2 |
| #24923309 | 2 |
| #24923265 | 2 |
| C2×#19128752 | 2 |
| #537×C167 | 2 |
| #3062 | 167 |