Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128235 | C2 | semidirect |
| 3. #19128002 | C2 | semidirect |
| 4. #19127997 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127937 | C2 | semidirect |
| 7. #19127930 | C2 | semidirect |
| 8. #19127917 | C2 | semidirect |
| 9. #19127902 | C2 | semidirect |
| 10. #19127897 | C2 | semidirect |
| 11. C2×C4⋊C8×C83 | C2 | semidirect |
| 142. C83 | #3247 | semidirect |
| 153. C2×C4⋊C8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128235 | 2 |
| #19128002 | 2 |
| #19127997 | 2 |
| #19127992 | 2 |
| #19127937 | 2 |
| #19127930 | 2 |
| #19127917 | 2 |
| #19127902 | 2 |
| #19127897 | 2 |
| C2×C4⋊C8×C83 | 2 |
| #3247 | 83 |