Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#14581825 | C2 | semidirect |
| 3. #19128277 | C2 | semidirect |
| 4. #19128181 | C2 | semidirect |
| 5. #19127924 | C2 | semidirect |
| 6. #19127917 | C2 | semidirect |
| 7. #19127912 | C2 | semidirect |
| 8. #19127907 | C2 | semidirect |
| 9. #19127703 | C2 | semidirect |
| 10. C2×#14581717 | C2 | semidirect |
| 11. #424×C83 | C2 | semidirect |
| 147. C83 | #3046 | semidirect |
| 156. #424 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581825 | 2 |
| C2×#14581814 | 2 |
| #19128277 | 2 |
| #19128181 | 2 |
| #19127924 | 2 |
| #19127917 | 2 |
| #19127912 | 2 |
| #19127907 | 2 |
| #19127703 | 2 |
| C2×#14581717 | 2 |
| #424×C83 | 2 |
| #3046 | 83 |