Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14581791 | C4 | semidirect |
| 10. #14581783 | C4 | semidirect |
| 38. C4×Dic83 | Q8 | semidirect |
| 48. C42×C83 | Q8 | semidirect |
| 87. C83 | #1994 | semidirect |
| 135. C42 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128254 | 2 |
| #19127724 | 2 |
| C42×Dic83 | 2 |
| #19127462 | 2 |
| #19127461 | 2 |
| #19127460 | 2 |
| #339×C83 | 2 |
| #1994 | 83 |