Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24908296 | C2 | semidirect |
| 2. #24906185 | C2 | semidirect |
| 3. #24906098 | C2 | semidirect |
| 4. #24905971 | C2 | semidirect |
| 6. #19127758 | C22 | semidirect |
| 7. #19127725 | C22 | semidirect |
| 9. #19127547 | C22 | semidirect |
| 16. #555×C83 | C4 | semidirect |
| 18. D42×C83 | C4 | semidirect |
| 160. C83 | #8491 | semidirect |
| 163. #555 | Dic83 | semidirect |
| 165. D42 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908296 | 2 |
| #24906185 | 2 |
| #24906098 | 2 |
| #24905971 | 2 |
| C83×#3549 | 2 |
| #8491 | 83 |