Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. #19128430 | C2 | semidirect |
| 4. #19128051 | C2 | semidirect |
| 5. #19128010 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. Q16×Dic83 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 116. C83 | #3364 | semidirect |
| 124. #462 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128430 | 2 |
| #19128425 | 2 |
| #19128057 | 2 |
| #19128051 | 2 |
| #19128010 | 2 |
| #19127982 | 2 |
| #19127925 | 2 |
| #19127825 | 2 |
| Q16×Dic83 | 2 |
| C4×#13050577 | 2 |
| #462×C83 | 2 |
| #3364 | 83 |