Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#19128857 | C2 | semidirect |
| 2. C2×#19128838 | C2 | semidirect |
| 3. #24923847 | C2 | semidirect |
| 4. #24923838 | C2 | semidirect |
| 5. #24923521 | C2 | semidirect |
| 6. #24923518 | C2 | semidirect |
| 7. #24923504 | C2 | semidirect |
| 8. #24923501 | C2 | semidirect |
| 9. #24923312 | C2 | semidirect |
| 10. C2×#19128754 | C2 | semidirect |
| 11. #416×C167 | C2 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 20. C2×C8×D167 | C22 | semidirect |
| 24. #19128808 | C22 | semidirect |
| 29. #19128803 | C22 | semidirect |
| 32. #19128765 | C22 | semidirect |
| 33. #19128763 | C22 | semidirect |
| 39. #103×C167 | C22 | semidirect |
| 40. #103×C167 | C22 | semidirect |
| 41. #102×C167 | C22 | semidirect |
| 42. #102×C167 | C22 | semidirect |
| 60. #14581934 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 162. #416 | D167 | semidirect |
| 189. #103 | C2×D167 | semidirect |
| 190. #103 | C2×D167 | semidirect |
| 193. #102 | C2×D167 | semidirect |
| 194. #102 | 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×#19128838 | 2 |
| #24923847 | 2 |
| #24923838 | 2 |
| #24923521 | 2 |
| #24923518 | 2 |
| #24923504 | 2 |
| #24923501 | 2 |
| #24923312 | 2 |
| C2×#19128754 | 2 |
| #416×C167 | 2 |
| #3062 | 167 |