Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. Q8×D332 | C2 | semidirect |
| 3. #19128053 | C2 | semidirect |
| 4. #19128044 | C2 | semidirect |
| 5. #19127948 | C2 | semidirect |
| 6. #19127907 | C2 | semidirect |
| 7. #19127841 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127778 | C2 | semidirect |
| 10. #19127708 | C2 | semidirect |
| 11. #477×C83 | C2 | semidirect |
| 127. C83 | #3329 | semidirect |
| 132. #477 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128417 | 2 |
| Q8×D332 | 2 |
| #19128053 | 2 |
| #19128044 | 2 |
| #19127948 | 2 |
| #19127907 | 2 |
| #19127841 | 2 |
| C4×#13050577 | 2 |
| #19127778 | 2 |
| #19127708 | 2 |
| #477×C83 | 2 |
| #3329 | 83 |