Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 163 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. #24918846 | C2 | semidirect |
| 3. #24906688 | C2 | semidirect |
| 4. #24906639 | C2 | semidirect |
| 5. #24906198 | C2 | semidirect |
| 6. #24905915 | C2 | semidirect |
| 7. C83×#3131 | C2 | semidirect |
| 17. #19127978 | C22 | semidirect |
| 19. #19127903 | C22 | semidirect |
| 21. #19127725 | C22 | semidirect |
| 22. #19127450 | C22 | semidirect |
| 24. #19127430 | C22 | semidirect |
| 25. #533×C83 | C22 | semidirect |
| 28. #487×C83 | C22 | semidirect |
| 31. C2×C4×C8×C83 | C22 | semidirect |
| 182. #3131 | D83 | semidirect |
| 187. C83 | #18691 | semidirect |
| 195. #533 | C2×D83 | semidirect |
| 199. #487 | C2×D83 | semidirect |
| 208. C2×C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921868 | 2 |
| #24918846 | 2 |
| #24906688 | 2 |
| #24906639 | 2 |
| #24906198 | 2 |
| #24905915 | 2 |
| C83×#3131 | 2 |
| #18691 | 83 |