Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 12. C2×Dic332 | C4 | semidirect |
| 84. C2×Dic83 | Q16 | semidirect |
| 120. C83 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic332 | 2 |
| C2×#14581757 | 2 |
| C2×#14581715 | 2 |
| #19127606 | 2 |
| #19127455 | 2 |
| #340×C83 | 2 |
| #1878 | 83 |