Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #19128429 | C2 | semidirect |
| 3. #19128073 | C2 | semidirect |
| 4. #19128072 | C2 | semidirect |
| 5. #19127907 | C2 | semidirect |
| 6. #19127904 | C2 | semidirect |
| 7. #19127900 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. #19127792 | C2 | semidirect |
| 10. C4×#13050577 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 102. Dic166 | SD16 | semidirect |
| 105. C83⋊C8 | #41 | semidirect |
| 129. C83 | #3392 | semidirect |
| 137. #460 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128429 | 2 |
| #19128371 | 2 |
| #19128073 | 2 |
| #19128072 | 2 |
| #19127907 | 2 |
| #19127904 | 2 |
| #19127900 | 2 |
| #19127825 | 2 |
| #19127792 | 2 |
| C4×#13050577 | 2 |
| #460×C83 | 2 |
| #3392 | 83 |