Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #19128105 | C2 | semidirect |
| 4. #19128050 | C2 | semidirect |
| 8. #19127995 | C2 | semidirect |
| 9. #19127994 | C2 | semidirect |
| 125. C83 | #3230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128253 | 2 |
| C2×#14581791 | 2 |
| #19128105 | 2 |
| #19128050 | 2 |
| #19128037 | 2 |
| #19128036 | 2 |
| #19128034 | 2 |
| #19127995 | 2 |
| #19127994 | 2 |
| #19127751 | 2 |
| #484×C83 | 2 |
| #3230 | 83 |