Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 44. #13050580 | Q8 | semidirect |
| 111. C83 | #3387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128111 | 2 |
| #19128097 | 2 |
| #19128005 | 2 |
| #19127996 | 2 |
| #19127986 | 2 |
| #19127983 | 2 |
| #19127832 | 2 |
| #19127806 | 2 |
| C4×#13050580 | 2 |
| #557×C83 | 2 |
| #3387 | 83 |