Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #24908294 | C2 | semidirect |
| 3. #24906183 | C2 | semidirect |
| 4. #24906097 | C2 | semidirect |
| 5. #24905972 | C2 | semidirect |
| 6. #24905971 | C2 | semidirect |
| 7. C83×#1557 | C2 | semidirect |
| 11. #19128416 | C4 | semidirect |
| 13. D4×D332 | C4 | semidirect |
| 20. #19127758 | C22 | semidirect |
| 22. #19127547 | C22 | semidirect |
| 29. #432×C83 | C22 | semidirect |
| 30. #423×C83 | C22 | semidirect |
| 237. #1557 | D83 | semidirect |
| 241. C83 | #8491 | semidirect |
| 256. #432 | C2×D83 | semidirect |
| 257. #423 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921868 | 2 |
| #24908294 | 2 |
| #24906183 | 2 |
| #24906097 | 2 |
| #24905972 | 2 |
| #24905971 | 2 |
| C83×#1557 | 2 |
| #8491 | 83 |