Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 438 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. #19128252 | C2 | semidirect |
| 2. #19128249 | C2 | semidirect |
| 3. #19128077 | C2 | semidirect |
| 4. #19128051 | C2 | semidirect |
| 5. #19128048 | C2 | semidirect |
| 6. #19127918 | C2 | semidirect |
| 7. #19127845 | C2 | semidirect |
| 8. #19127752 | C2 | semidirect |
| 9. #492×C83 | C2 | semidirect |
| 121. C83 | #3207 | semidirect |
| 125. #492 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128249 | 2 |
| #19128077 | 2 |
| #19128051 | 2 |
| #19128048 | 2 |
| #19127918 | 2 |
| #19127845 | 2 |
| #19127752 | 2 |
| #492×C83 | 2 |
| #3207 | 83 |