Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128424 | C2 | semidirect |
| 3. #19128048 | C2 | semidirect |
| 4. #19128027 | C2 | semidirect |
| 5. #19127981 | C2 | semidirect |
| 6. #19127950 | C2 | semidirect |
| 7. #19127901 | C2 | semidirect |
| 8. #19127850 | C2 | semidirect |
| 9. #19127780 | C2 | semidirect |
| 10. #19127704 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 14. C2×#13050577 | C22 | semidirect |
| 15. C2×#13050573 | C22 | semidirect |
| 16. #14581792 | C22 | semidirect |
| 20. #14581768 | C22 | semidirect |
| 26. #14581750 | C22 | semidirect |
| 27. #14581725 | C22 | semidirect |
| 28. C4⋊(C83⋊C8) | C22 | semidirect |
| 29. #14581714 | C22 | semidirect |
| 30. #14581714 | C22 | semidirect |
| 32. #14581712 | C22 | semidirect |
| 33. (C2×D83)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C83 | C22 | semidirect |
| 37. #106×C83 | C22 | semidirect |
| 38. #103×C83 | C22 | semidirect |
| 40. C4×C8×C83 | C22 | semidirect |
| 136. C83 | #3324 | semidirect |
| 145. C4×SD16 | D83 | semidirect |
| 162. C4×Q8 | C2×D83 | semidirect |
| 167. #106 | C2×D83 | semidirect |
| 169. #103 | C2×D83 | semidirect |
| 176. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128424 | 2 |
| D4×D332 | 2 |
| #19128048 | 2 |
| #19128027 | 2 |
| #19127981 | 2 |
| #19127950 | 2 |
| #19127901 | 2 |
| #19127850 | 2 |
| #19127780 | 2 |
| #19127704 | 2 |
| C4×SD16×C83 | 2 |
| #3324 | 83 |