Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #19128107 | C2 | semidirect |
| 3. #19128104 | C2 | semidirect |
| 4. #19128008 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 11. Q82×C83 | C2 | semidirect |
| 45. #13050577 | Q8 | semidirect |
| 116. C83 | #3385 | semidirect |
| 117. Q82 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| #19128107 | 2 |
| #19128104 | 2 |
| #19128008 | 2 |
| #19127996 | 2 |
| #19127988 | 2 |
| #19127978 | 2 |
| #19127832 | 2 |
| #19127799 | 2 |
| C4×#13050577 | 2 |
| Q82×C83 | 2 |
| #3385 | 83 |