Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128429 | C2 | semidirect |
| 3. #19128068 | C2 | semidirect |
| 4. #19128053 | C2 | semidirect |
| 5. #19128007 | C2 | semidirect |
| 8. #19127828 | C2 | semidirect |
| 11. #477×C83 | C2 | semidirect |
| 117. C83 | #3372 | semidirect |
| 123. #477 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128429 | 2 |
| #19128412 | 2 |
| #19128068 | 2 |
| #19128053 | 2 |
| #19128007 | 2 |
| #19127907 | 2 |
| #19127905 | 2 |
| #19127828 | 2 |
| #19127800 | 2 |
| C4×#13050577 | 2 |
| #477×C83 | 2 |
| #3372 | 83 |