Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D83 | C2 | semidirect |
| 3. #19128095 | C2 | semidirect |
| 4. #19128093 | C2 | semidirect |
| 5. #19128071 | C2 | semidirect |
| 6. #19127910 | C2 | semidirect |
| 7. #19127905 | C2 | semidirect |
| 8. #19127858 | C2 | semidirect |
| 10. #19127756 | C2 | semidirect |
| 11. #491×C83 | C2 | semidirect |
| 136. C83 | #3218 | semidirect |
| 142. #491 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D83 | 2 |
| #19128236 | 2 |
| #19128095 | 2 |
| #19128093 | 2 |
| #19128071 | 2 |
| #19127910 | 2 |
| #19127905 | 2 |
| #19127858 | 2 |
| #19127841 | 2 |
| #19127756 | 2 |
| #491×C83 | 2 |
| #3218 | 83 |