Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19128421 | C2 | semidirect |
| 2. #19128097 | C2 | semidirect |
| 3. #19128042 | C2 | semidirect |
| 4. #19128022 | C2 | semidirect |
| 5. #19127993 | C2 | semidirect |
| 6. #19127981 | C2 | semidirect |
| 7. #19127928 | C2 | semidirect |
| 8. C4×#13050578 | C2 | semidirect |
| 9. D4×C83⋊C8 | C2 | semidirect |
| 10. #19127737 | C2 | semidirect |
| 121. C83 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128421 | 2 |
| #19128097 | 2 |
| #19128042 | 2 |
| #19128022 | 2 |
| #19127993 | 2 |
| #19127981 | 2 |
| #19127928 | 2 |
| C4×#13050578 | 2 |
| D4×C83⋊C8 | 2 |
| #19127737 | 2 |
| #555×C83 | 2 |
| #3340 | 83 |