Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. C2×C8×Dic83 | C2 | semidirect |
| 5. #19127465 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 7. #405×C83 | C2 | semidirect |
| 10. #14581798 | C4 | semidirect |
| 16. #14581718 | C4 | semidirect |
| 17. #14581715 | C4 | semidirect |
| 18. #14581712 | C4 | semidirect |
| 99. C83 | #1764 | semidirect |
| 103. #405 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581798 | 2 |
| C2×#14581718 | 2 |
| #19127695 | 2 |
| C2×C8×Dic83 | 2 |
| #19127465 | 2 |
| #19127460 | 2 |
| #405×C83 | 2 |
| #1764 | 83 |