Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×#13050579 | C2 | semidirect |
| 3. #19128277 | C2 | semidirect |
| 4. #19128175 | C2 | semidirect |
| 5. #19127917 | C2 | semidirect |
| 6. #19127907 | C2 | semidirect |
| 7. #19127711 | C2 | semidirect |
| 8. #19127698 | C2 | semidirect |
| 9. #424×C83 | C2 | semidirect |
| 18. #14581792 | C22 | semidirect |
| 19. #14581780 | C22 | semidirect |
| 26. #14581717 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 28. #14581714 | C22 | semidirect |
| 32. C4⋊C8×C83 | C22 | semidirect |
| 117. C83 | #3042 | semidirect |
| 124. #424 | D83 | semidirect |
| 146. 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×#14581820 | 2 |
| C22×#13050579 | 2 |
| #19128277 | 2 |
| #19128175 | 2 |
| #19127917 | 2 |
| #19127907 | 2 |
| #19127711 | 2 |
| #19127698 | 2 |
| #424×C83 | 2 |
| #3042 | 83 |