Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #19128424 | C2 | semidirect |
| 3. #19128099 | C2 | semidirect |
| 4. #19128040 | C2 | semidirect |
| 5. #19128024 | C2 | semidirect |
| 6. #19127996 | C2 | semidirect |
| 7. #19127981 | C2 | semidirect |
| 8. #19127927 | C2 | semidirect |
| 9. C8×D332 | C2 | semidirect |
| 10. #19127736 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 121. C83 | #3340 | semidirect |
| 130. C4×SD16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128424 | 2 |
| #19128416 | 2 |
| #19128099 | 2 |
| #19128040 | 2 |
| #19128024 | 2 |
| #19127996 | 2 |
| #19127981 | 2 |
| #19127927 | 2 |
| C8×D332 | 2 |
| #19127736 | 2 |
| C4×SD16×C83 | 2 |
| #3340 | 83 |