Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. C4×#13050590 | C2 | semidirect |
| 2. #19128022 | C2 | semidirect |
| 3. #19127983 | C2 | semidirect |
| 4. #19127978 | C2 | semidirect |
| 5. #19127898 | C2 | semidirect |
| 6. #19127893 | C2 | semidirect |
| 7. #19127844 | C2 | semidirect |
| 8. #19127811 | C2 | semidirect |
| 9. #19127801 | C2 | semidirect |
| 10. #19127758 | C2 | semidirect |
| 11. #532×C83 | C2 | semidirect |
| 109. D332 | #41 | semidirect |
| 114. Dic166 | #41 | semidirect |
| 145. C83 | #3115 | semidirect |
| 146. #532 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13050590 | 2 |
| #19128022 | 2 |
| #19127983 | 2 |
| #19127978 | 2 |
| #19127898 | 2 |
| #19127893 | 2 |
| #19127844 | 2 |
| #19127811 | 2 |
| #19127801 | 2 |
| #19127758 | 2 |
| #532×C83 | 2 |
| #3115 | 83 |