Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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. #19127831 | C2 | semidirect |
| 3. #19127830 | C2 | semidirect |
| 4. #19127829 | C2 | semidirect |
| 5. #19127828 | C2 | semidirect |
| 92. C83 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128254 | 2 |
| #19127831 | 2 |
| #19127830 | 2 |
| #19127829 | 2 |
| #19127828 | 2 |
| #19127762 | 2 |
| #19127759 | 2 |
| #19127755 | 2 |
| #433×C83 | 2 |
| #2987 | 83 |