Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #19128304 | C2 | semidirect |
| 2. #19128102 | C2 | semidirect |
| 3. #19128076 | C2 | semidirect |
| 4. #19128064 | C2 | semidirect |
| 5. #19127952 | C2 | semidirect |
| 6. #19127937 | C2 | semidirect |
| 7. #19127810 | C2 | semidirect |
| 8. D8×Dic83 | C2 | semidirect |
| 9. #19127783 | C2 | semidirect |
| 10. #19127656 | C2 | semidirect |
| 11. #466×C83 | C2 | semidirect |
| 124. C83 | #3176 | semidirect |
| 131. #466 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128304 | 2 |
| #19128102 | 2 |
| #19128076 | 2 |
| #19128064 | 2 |
| #19127952 | 2 |
| #19127937 | 2 |
| #19127810 | 2 |
| D8×Dic83 | 2 |
| #19127783 | 2 |
| #19127656 | 2 |
| #466×C83 | 2 |
| #3176 | 83 |