Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4⋊Q8×D83 | C2 | semidirect |
| 3. #19128072 | C2 | semidirect |
| 4. #19128050 | C2 | semidirect |
| 5. #19127907 | C2 | semidirect |
| 6. #19127906 | C2 | semidirect |
| 7. #19127903 | C2 | semidirect |
| 8. #19127841 | C2 | semidirect |
| 9. #19127838 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #461×C83 | C2 | semidirect |
| 114. C4×D83 | SD16 | semidirect |
| 149. C83 | #3206 | semidirect |
| 157. #461 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128248 | 2 |
| C4⋊Q8×D83 | 2 |
| #19128072 | 2 |
| #19128050 | 2 |
| #19127907 | 2 |
| #19127906 | 2 |
| #19127903 | 2 |
| #19127841 | 2 |
| #19127838 | 2 |
| #19127753 | 2 |
| #461×C83 | 2 |
| #3206 | 83 |