Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 171 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. #24917952 | C2 | semidirect |
| 3. #24916315 | C2 | semidirect |
| 4. #24909520 | C2 | semidirect |
| 5. #24909506 | C2 | semidirect |
| 6. #24909221 | C2 | semidirect |
| 7. #24909183 | C2 | semidirect |
| 8. #24909171 | C2 | semidirect |
| 9. C22×SD32×C83 | C2 | semidirect |
| 19. #19128086 | C22 | semidirect |
| 20. #19128079 | C22 | semidirect |
| 26. Dic83⋊C16 | C22 | semidirect |
| 27. #19127506 | C22 | semidirect |
| 28. #19127505 | C22 | semidirect |
| 29. #19127503 | C22 | semidirect |
| 178. C22×SD32 | D83 | semidirect |
| 186. C83 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128137 | 2 |
| #24917952 | 2 |
| #24916315 | 2 |
| #24909520 | 2 |
| #24909506 | 2 |
| #24909221 | 2 |
| #24909183 | 2 |
| #24909171 | 2 |
| C22×SD32×C83 | 2 |
| #33586 | 83 |