Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128251 | C2 | semidirect |
| 2. #19128088 | C2 | semidirect |
| 3. #19128063 | C2 | semidirect |
| 4. #19127906 | C2 | semidirect |
| 5. #19127896 | C2 | semidirect |
| 6. #19127844 | C2 | semidirect |
| 7. #19127758 | C2 | semidirect |
| 8. #532×C83 | C2 | semidirect |
| 118. C83 | #3214 | semidirect |
| 120. #532 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128088 | 2 |
| #19128063 | 2 |
| #19127906 | 2 |
| #19127896 | 2 |
| #19127844 | 2 |
| #19127758 | 2 |
| #532×C83 | 2 |
| #3214 | 83 |