Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #19127799 | C2 | semidirect |
| 4. C4×#13050577 | C2 | semidirect |
| 5. #19127737 | C2 | semidirect |
| 6. #19127710 | C2 | semidirect |
| 8. #19127657 | C2 | semidirect |
| 9. #519×C83 | C2 | semidirect |
| 11. C2×#13050577 | C4 | semidirect |
| 20. #14581725 | C22 | semidirect |
| 21. #14581723 | C22 | semidirect |
| 22. #14581716 | C22 | semidirect |
| 24. #14581703 | C22 | semidirect |
| 25. C4×C83⋊C8 | C22 | semidirect |
| 28. C4×Q8×C83 | C22 | semidirect |
| 38. #13050577 | C2×C4 | semidirect |
| 39. #13050577 | C2×C4 | semidirect |
| 41. C2×C83⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C83 | C2×C4 | semidirect |
| 104. C83 | #2949 | semidirect |
| 106. #519 | D83 | semidirect |
| 122. C4×Q8 | C2×D83 | semidirect |
| 139. C2×Q8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050577 | 2 |
| #19128175 | 2 |
| #19127799 | 2 |
| C4×#13050577 | 2 |
| #19127737 | 2 |
| #19127710 | 2 |
| #19127705 | 2 |
| #19127657 | 2 |
| #519×C83 | 2 |
| #2949 | 83 |