Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 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 |
|---|---|---|
| 1. #24918466 | C2 | semidirect |
| 2. #24917849 | C2 | semidirect |
| 3. #24906769 | C2 | semidirect |
| 4. #24906087 | C2 | semidirect |
| 5. #24906061 | C2 | semidirect |
| 7. #19128258 | C22 | semidirect |
| 8. #19128096 | C22 | semidirect |
| 9. #19128060 | C22 | semidirect |
| 10. #19128060 | C22 | semidirect |
| 15. #19127758 | C22 | semidirect |
| 18. C4×#13050574 | C22 | semidirect |
| 19. #19127441 | C22 | semidirect |
| 20. #19127441 | C22 | semidirect |
| 33. #14581792 | C23 | semidirect |
| 44. #14581703 | C23 | semidirect |
| 45. #14581703 | C23 | semidirect |
| 189. C83 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918466 | 2 |
| #24917849 | 2 |
| #24906769 | 2 |
| #24906087 | 2 |
| #24906061 | 2 |
| C2×H(3,𝔽4)×C83 | 2 |
| #18997 | 83 |