Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #19128429 | C2 | semidirect |
| 3. #19128092 | C2 | semidirect |
| 5. #19127922 | C2 | semidirect |
| 6. #19127912 | C2 | semidirect |
| 7. #19127904 | C2 | semidirect |
| 8. #19127828 | C2 | semidirect |
| 9. #19127798 | C2 | semidirect |
| 10. C4×#13050580 | 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 |
| #19128429 | 2 |
| #19128092 | 2 |
| #19128073 | 2 |
| #19127922 | 2 |
| #19127912 | 2 |
| #19127904 | 2 |
| #19127828 | 2 |
| #19127798 | 2 |
| C4×#13050580 | 2 |
| #460×C83 | 2 |
| #3400 | 83 |