Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14581780 | C2 | semidirect |
| 2. #19128083 | C2 | semidirect |
| 3. #19128058 | C2 | semidirect |
| 4. #19127923 | C2 | semidirect |
| 5. #19127916 | C2 | semidirect |
| 6. #19127856 | C2 | semidirect |
| 7. #19127851 | C2 | semidirect |
| 8. #19127839 | C2 | semidirect |
| 10. #19127754 | C2 | semidirect |
| 11. #529×C83 | C2 | semidirect |
| 14. C2×#13050580 | C22 | semidirect |
| 15. C2×#13050578 | C22 | semidirect |
| 24. C4⋊(C83⋊C8) | C22 | semidirect |
| 25. #14581715 | C22 | semidirect |
| 26. #14581715 | C22 | semidirect |
| 31. C4×C83⋊C8 | C22 | semidirect |
| 33. #125×C83 | C22 | semidirect |
| 34. #124×C83 | C22 | semidirect |
| 38. C4×Q8×C83 | C22 | semidirect |
| 40. C4×D4×C83 | C22 | semidirect |
| 144. C83 | #3211 | semidirect |
| 145. #529 | D83 | semidirect |
| 163. #125 | C2×D83 | semidirect |
| 168. #124 | C2×D83 | semidirect |
| 172. C4×Q8 | C2×D83 | semidirect |
| 174. C4×D4 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581780 | 2 |
| #19128083 | 2 |
| #19128058 | 2 |
| #19127923 | 2 |
| #19127916 | 2 |
| #19127856 | 2 |
| #19127851 | 2 |
| #19127839 | 2 |
| #19127834 | 2 |
| #19127754 | 2 |
| #529×C83 | 2 |
| #3211 | 83 |