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 |
|---|---|---|
| 2. #19127724 | C2 | semidirect |
| 3. C2×#14581710 | C2 | semidirect |
| 4. C2×#14581710 | C2 | semidirect |
| 6. M16×Dic83 | C2 | semidirect |
| 109. C83 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581779 | 2 |
| #19127724 | 2 |
| C2×#14581710 | 2 |
| C2×#14581709 | 2 |
| M16×Dic83 | 2 |
| C2×#100×C83 | 2 |
| #1967 | 83 |