Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 2. Q8×Dic166 | C2 | semidirect |
| 3. #19128059 | C2 | semidirect |
| 5. #19127997 | C2 | semidirect |
| 6. #19127979 | C2 | semidirect |
| 7. #19127921 | C2 | semidirect |
| 8. #19127828 | C2 | semidirect |
| 9. #19127802 | C2 | semidirect |
| 10. C4×#13050580 | C2 | semidirect |
| 119. C83 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| Q8×Dic166 | 2 |
| #19128059 | 2 |
| #19128047 | 2 |
| #19127997 | 2 |
| #19127979 | 2 |
| #19127921 | 2 |
| #19127828 | 2 |
| #19127802 | 2 |
| C4×#13050580 | 2 |
| #460×C83 | 2 |
| #3375 | 83 |