Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128251 | C2 | semidirect |
| 2. #19128111 | C2 | semidirect |
| 3. #19128091 | C2 | semidirect |
| 4. #19128067 | C2 | semidirect |
| 5. #19128060 | C2 | semidirect |
| 6. #19127935 | C2 | semidirect |
| 7. #19127932 | C2 | semidirect |
| 8. #19127811 | C2 | semidirect |
| 9. #19127799 | C2 | semidirect |
| 10. C2×#14581703 | C2 | semidirect |
| 11. #529×C83 | C2 | semidirect |
| 110. C83⋊C8 | #41 | semidirect |
| 138. C83 | #3180 | semidirect |
| 140. #529 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128111 | 2 |
| #19128091 | 2 |
| #19128067 | 2 |
| #19128060 | 2 |
| #19127935 | 2 |
| #19127932 | 2 |
| #19127811 | 2 |
| #19127799 | 2 |
| C2×#14581703 | 2 |
| #529×C83 | 2 |
| #3180 | 83 |