Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128320 | C2 | semidirect |
| 2. #19128106 | C2 | semidirect |
| 3. #19128060 | C2 | semidirect |
| 4. #19127944 | C2 | semidirect |
| 5. #19127939 | C2 | semidirect |
| 7. #19127802 | C2 | semidirect |
| 8. Q16×Dic83 | C2 | semidirect |
| 9. D8×Dic83 | C2 | semidirect |
| 10. #19127655 | C2 | semidirect |
| 11. #495×C83 | C2 | semidirect |
| 118. C83 | #3175 | semidirect |
| 121. #495 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128320 | 2 |
| #19128106 | 2 |
| #19128060 | 2 |
| #19127944 | 2 |
| #19127939 | 2 |
| #19127934 | 2 |
| #19127802 | 2 |
| Q16×Dic83 | 2 |
| D8×Dic83 | 2 |
| #19127655 | 2 |
| #495×C83 | 2 |
| #3175 | 83 |