Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19128248 | C2 | semidirect |
| 2. #127×D83 | C2 | semidirect |
| 3. #19128076 | C2 | semidirect |
| 4. #19128046 | C2 | semidirect |
| 5. #19127897 | C2 | semidirect |
| 6. #19127896 | C2 | semidirect |
| 7. #19127893 | C2 | semidirect |
| 8. #19127836 | C2 | semidirect |
| 9. #19127833 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #459×C83 | C2 | semidirect |
| 16. C2×D664 | C22 | semidirect |
| 17. C2×#13050575 | C22 | semidirect |
| 18. C2×#13050575 | C22 | semidirect |
| 19. #14581791 | C22 | semidirect |
| 24. #14581788 | C22 | semidirect |
| 29. C4×D332 | C22 | semidirect |
| 32. C4⋊(C83⋊C8) | C22 | semidirect |
| 33. #14581714 | C22 | semidirect |
| 34. #14581713 | C22 | semidirect |
| 35. #14581712 | C22 | semidirect |
| 37. C8×Dic83 | C22 | semidirect |
| 38. C2×D8×C83 | C22 | semidirect |
| 40. C4×D4×C83 | C22 | semidirect |
| 41. C4⋊C8×C83 | C22 | semidirect |
| 42. #102×C83 | C22 | semidirect |
| 127. C4×D83 | D8 | semidirect |
| 166. C83 | #3205 | semidirect |
| 174. #459 | D83 | semidirect |
| 185. C2×D8 | C2×D83 | semidirect |
| 199. C4×D4 | C2×D83 | semidirect |
| 202. C4⋊C8 | C2×D83 | semidirect |
| 206. #102 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128248 | 2 |
| #127×D83 | 2 |
| #19128076 | 2 |
| #19128046 | 2 |
| #19127897 | 2 |
| #19127896 | 2 |
| #19127893 | 2 |
| #19127836 | 2 |
| #19127833 | 2 |
| #19127753 | 2 |
| #459×C83 | 2 |
| #3205 | 83 |