Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D83 | C2 | semidirect |
| 3. #24909706 | C2 | semidirect |
| 4. #24909705 | C2 | semidirect |
| 5. #24909704 | C2 | semidirect |
| 6. #24909703 | C2 | semidirect |
| 7. #357×D83 | C2 | semidirect |
| 8. #346×D83 | C2 | semidirect |
| 9. C83×#2244 | C2 | semidirect |
| 15. #19128103 | C22 | semidirect |
| 16. #19128102 | C22 | semidirect |
| 26. #19127503 | C22 | semidirect |
| 27. #19127502 | C22 | semidirect |
| 28. #19127501 | C22 | semidirect |
| 29. #19127477 | C22 | semidirect |
| 30. #19127476 | C22 | semidirect |
| 31. #499×C83 | C22 | semidirect |
| 33. #357×C83 | C22 | semidirect |
| 34. #346×C83 | C22 | semidirect |
| 155. D83 | #2244 | direct (N × H) |
| 162. #2244 | D83 | direct (N × H) |
| 165. C83 | C2×#2244 | semidirect |
| 175. #499 | C2×D83 | semidirect |
| 187. #357 | C2×D83 | semidirect |
| 190. #346 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D83 | 2 |
| #493×D83 | 2 |
| #24909706 | 2 |
| #24909705 | 2 |
| #24909704 | 2 |
| #24909703 | 2 |
| #357×D83 | 2 |
| #346×D83 | 2 |
| C83×#2244 | 2 |
| C2×#2244 | 83 |