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 |
|---|---|---|
| 2. #19128426 | C2 | semidirect |
| 3. #19128092 | C2 | semidirect |
| 4. #19127921 | C2 | semidirect |
| 5. #19127908 | C2 | semidirect |
| 6. #19127904 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 9. #19127802 | C2 | semidirect |
| 10. C4×Dic332 | C2 | semidirect |
| 122. C83 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128426 | 2 |
| #19128092 | 2 |
| #19127921 | 2 |
| #19127908 | 2 |
| #19127904 | 2 |
| #19127898 | 2 |
| #19127831 | 2 |
| #19127802 | 2 |
| C4×Dic332 | 2 |
| #492×C83 | 2 |
| #3400 | 83 |