Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #19128306 | C2 | semidirect |
| 2. #19128002 | C2 | semidirect |
| 3. #19127954 | C2 | semidirect |
| 4. #19127937 | C2 | semidirect |
| 5. #19127897 | C2 | semidirect |
| 6. #424×C83 | C2 | semidirect |
| 72. C83 | #3259 | semidirect |
| 78. #424 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128306 | 2 |
| #19128002 | 2 |
| #19127954 | 2 |
| #19127937 | 2 |
| #19127897 | 2 |
| #424×C83 | 2 |
| #3259 | 83 |