Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#14581717 | C2 | semidirect |
| 5. C2×#14581710 | C2 | semidirect |
| 6. #19127469 | C2 | semidirect |
| 7. #341×C83 | C2 | semidirect |
| 11. #14581825 | C4 | semidirect |
| 117. C83 | #1908 | semidirect |
| 124. #341 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581825 | 2 |
| C2×#14581798 | 2 |
| #19127703 | 2 |
| C2×#14581717 | 2 |
| C2×#14581710 | 2 |
| #19127469 | 2 |
| #341×C83 | 2 |
| #1908 | 83 |