Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14581817 | C2 | semidirect |
| 2. C22×#13050575 | C2 | semidirect |
| 3. #19128175 | C2 | semidirect |
| 4. #19127913 | C2 | semidirect |
| 5. #19127893 | C2 | semidirect |
| 6. #19127728 | C2 | semidirect |
| 7. #19127706 | C2 | semidirect |
| 8. #19127697 | C2 | semidirect |
| 9. #535×C83 | C2 | semidirect |
| 12. C2×#13050577 | C22 | semidirect |
| 15. C2×#13050575 | C22 | semidirect |
| 18. C4×D332 | C22 | semidirect |
| 22. C4⋊(C83⋊C8) | C22 | semidirect |
| 23. #14581716 | C22 | semidirect |
| 24. #14581713 | C22 | semidirect |
| 25. #14581713 | C22 | semidirect |
| 28. #127×C83 | C22 | semidirect |
| 29. #124×C83 | C22 | semidirect |
| 36. C2×D332 | D4 | semidirect |
| 122. C83 | #3041 | semidirect |
| 125. #535 | D83 | semidirect |
| 142. #127 | C2×D83 | semidirect |
| 143. #124 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581817 | 2 |
| C22×#13050575 | 2 |
| #19128175 | 2 |
| #19127913 | 2 |
| #19127893 | 2 |
| #19127728 | 2 |
| #19127706 | 2 |
| #19127697 | 2 |
| #535×C83 | 2 |
| #3041 | 83 |