Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 1. #19128251 | C2 | semidirect |
| 2. #19128083 | C2 | semidirect |
| 3. #19128058 | C2 | semidirect |
| 4. #19127911 | C2 | semidirect |
| 5. #19127906 | C2 | semidirect |
| 6. #19127901 | C2 | semidirect |
| 7. #19127896 | C2 | semidirect |
| 8. #19127861 | C2 | semidirect |
| 9. #19127844 | C2 | semidirect |
| 10. #19127754 | C2 | semidirect |
| 11. #529×C83 | C2 | semidirect |
| 145. C83 | #3212 | semidirect |
| 147. #529 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128083 | 2 |
| #19128058 | 2 |
| #19127911 | 2 |
| #19127906 | 2 |
| #19127901 | 2 |
| #19127896 | 2 |
| #19127861 | 2 |
| #19127844 | 2 |
| #19127754 | 2 |
| #529×C83 | 2 |
| #3212 | 83 |