Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #19128052 | C2 | semidirect |
| 4. #19128038 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 6. #19127941 | C2 | semidirect |
| 7. #19127911 | C2 | semidirect |
| 8. #19127855 | C2 | semidirect |
| 10. #103×D83 | C2 | semidirect |
| 11. C4×Q16×C83 | C2 | semidirect |
| 91. D332 | Q16 | semidirect |
| 123. C83 | #3299 | semidirect |
| 132. C4×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| Q8×D332 | 2 |
| #19128052 | 2 |
| #19128038 | 2 |
| #19127996 | 2 |
| #19127941 | 2 |
| #19127911 | 2 |
| #19127855 | 2 |
| C8×D332 | 2 |
| #103×D83 | 2 |
| C4×Q16×C83 | 2 |
| #3299 | 83 |