Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #19127987 | C2 | semidirect |
| 4. #19127986 | C2 | semidirect |
| 5. #19127984 | C2 | semidirect |
| 8. #19127909 | C2 | semidirect |
| 9. #19127908 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 130. C83 | #3255 | 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 |
| #19128255 | 2 |
| #19127987 | 2 |
| #19127986 | 2 |
| #19127984 | 2 |
| #19127958 | 2 |
| #19127956 | 2 |
| #19127909 | 2 |
| #19127908 | 2 |
| #19127723 | 2 |
| #462×C83 | 2 |
| #3255 | 83 |