Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#14581727 | C2 | semidirect |
| 3. #19127728 | C2 | semidirect |
| 6. #19127456 | C2 | semidirect |
| 7. #339×C83 | C2 | semidirect |
| 20. #14581715 | C4 | semidirect |
| 21. #14581715 | C4 | semidirect |
| 22. #14581712 | C4 | semidirect |
| 23. #14581712 | C4 | semidirect |
| 110. C83 | #1866 | semidirect |
| 116. #339 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581800 | 2 |
| C2×#14581727 | 2 |
| #19127728 | 2 |
| C2×#14581720 | 2 |
| #19127695 | 2 |
| #19127456 | 2 |
| #339×C83 | 2 |
| #1866 | 83 |