Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #19128252 | C2 | semidirect |
| 2. C4×D4×D83 | C2 | semidirect |
| 3. #19128016 | C2 | semidirect |
| 4. #19127978 | C2 | semidirect |
| 5. #19127897 | C2 | semidirect |
| 6. #19127896 | C2 | semidirect |
| 7. #19127836 | C2 | semidirect |
| 8. #19127783 | C2 | semidirect |
| 9. #19127781 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 17. #14581789 | C22 | semidirect |
| 25. #14581754 | C22 | semidirect |
| 31. #14581725 | C22 | semidirect |
| 32. C4⋊(C83⋊C8) | C22 | semidirect |
| 33. #14581714 | C22 | semidirect |
| 35. #14581712 | C22 | semidirect |
| 37. C8×Dic83 | C22 | semidirect |
| 38. C4⋊Q8×C83 | C22 | semidirect |
| 40. #107×C83 | C22 | semidirect |
| 41. C4⋊C8×C83 | C22 | semidirect |
| 93. D4×C83 | #41 | semidirect |
| 112. D332 | #41 | semidirect |
| 120. C4×D83 | D8 | semidirect |
| 155. C83 | #3100 | semidirect |
| 160. #474 | D83 | semidirect |
| 172. C4⋊Q8 | C2×D83 | semidirect |
| 189. #107 | C2×D83 | semidirect |
| 191. C4⋊C8 | C2×D83 | semidirect |
| 256. D4 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| C4×D4×D83 | 2 |
| #19128016 | 2 |
| #19127978 | 2 |
| #19127897 | 2 |
| #19127896 | 2 |
| #19127836 | 2 |
| #19127783 | 2 |
| #19127781 | 2 |
| #19127753 | 2 |
| #474×C83 | 2 |
| #3100 | 83 |