Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19127987 | C2 | semidirect |
| 5. #19127986 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 8. #19127808 | C2 | semidirect |
| 9. #19127805 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 133. C83 | #3113 | semidirect |
| 140. #462 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4×Q8×D83 | 2 |
| #19128030 | 2 |
| #19127987 | 2 |
| #19127986 | 2 |
| #19127908 | 2 |
| #19127855 | 2 |
| #19127808 | 2 |
| #19127805 | 2 |
| #19127757 | 2 |
| #462×C83 | 2 |
| #3113 | 83 |