Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#14581815 | C2 | semidirect |
| 2. C2×D8×D83 | C2 | semidirect |
| 3. #19128344 | C2 | semidirect |
| 4. #19127939 | C2 | semidirect |
| 5. #19127934 | C2 | semidirect |
| 6. #19127913 | C2 | semidirect |
| 7. #19127850 | C2 | semidirect |
| 8. #19127845 | C2 | semidirect |
| 9. C4×D664 | C2 | semidirect |
| 10. C8×D332 | C2 | semidirect |
| 11. #495×C83 | C2 | semidirect |
| 12. C2×#13050591 | C22 | semidirect |
| 15. C2×#13050577 | C22 | semidirect |
| 20. C2×C8×D83 | C22 | semidirect |
| 24. #14581763 | C22 | semidirect |
| 27. C4×D332 | C22 | semidirect |
| 29. #14581726 | C22 | semidirect |
| 30. C4⋊(C83⋊C8) | C22 | semidirect |
| 31. #14581716 | C22 | semidirect |
| 32. #14581714 | C22 | semidirect |
| 33. #14581713 | C22 | semidirect |
| 35. (C2×D83)⋊C8 | C22 | semidirect |
| 36. C2×Q16×C83 | C22 | semidirect |
| 37. C2×SD16×C83 | C22 | semidirect |
| 39. #124×C83 | C22 | semidirect |
| 40. C4×C8×C83 | C22 | semidirect |
| 56. D664 | D4 | semidirect |
| 127. C2×D83 | #135 | semidirect |
| 144. C83 | #3280 | semidirect |
| 148. #495 | D83 | semidirect |
| 159. C2×Q16 | C2×D83 | semidirect |
| 161. C2×SD16 | C2×D83 | semidirect |
| 168. #124 | C2×D83 | semidirect |
| 184. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581815 | 2 |
| C2×D8×D83 | 2 |
| #19128344 | 2 |
| #19127939 | 2 |
| #19127934 | 2 |
| #19127913 | 2 |
| #19127850 | 2 |
| #19127845 | 2 |
| C4×D664 | 2 |
| C8×D332 | 2 |
| #495×C83 | 2 |
| #3280 | 83 |