Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
312 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. C2×Dic332 | C4 | semidirect |
| 42. C2×C4×C83 | Q16 | semidirect |
| 78. C83 | #1969 | semidirect |
| 129. C2×C4 | Dic332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic332 | 2 |
| C2×#14581726 | 2 |
| C2×#14581717 | 2 |
| #19127607 | 2 |
| C2×C4×C8×C83 | 2 |
| #1969 | 83 |