Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 392 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. #19128252 | C2 | semidirect |
| 2. #19128238 | C2 | semidirect |
| 3. #19128000 | C2 | semidirect |
| 4. #19127978 | C2 | semidirect |
| 5. #19127955 | C2 | semidirect |
| 6. #19127950 | C2 | semidirect |
| 7. #19127919 | C2 | semidirect |
| 8. #19127901 | C2 | semidirect |
| 9. #19127897 | C2 | semidirect |
| 10. #19127723 | C2 | semidirect |
| 11. #475×C83 | C2 | semidirect |
| 142. C83 | #3251 | semidirect |
| 146. #475 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128238 | 2 |
| #19128000 | 2 |
| #19127978 | 2 |
| #19127955 | 2 |
| #19127950 | 2 |
| #19127919 | 2 |
| #19127901 | 2 |
| #19127897 | 2 |
| #19127723 | 2 |
| #475×C83 | 2 |
| #3251 | 83 |