Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 31. C2×Dic166 | Q8 | semidirect |
| 105. C83 | #2028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19127711 | 2 |
| #19127709 | 2 |
| #19127607 | 2 |
| #19127469 | 2 |
| #19127461 | 2 |
| #339×C83 | 2 |
| #2028 | 83 |