Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
366 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 366 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. #19128399 | C2 | semidirect |
| 2. #19128102 | C2 | semidirect |
| 3. #19128028 | C2 | semidirect |
| 4. #19128019 | C2 | semidirect |
| 5. #19128004 | C2 | semidirect |
| 6. #19127938 | C2 | semidirect |
| 7. #19127937 | C2 | semidirect |
| 8. #19127783 | C2 | semidirect |
| 9. C8×C22⋊D83 | C2 | semidirect |
| 10. #19127738 | C2 | semidirect |
| 11. C2×#107×C83 | C2 | semidirect |
| 121. C83 | #3339 | semidirect |
| 132. C2×#107 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128399 | 2 |
| #19128102 | 2 |
| #19128028 | 2 |
| #19128019 | 2 |
| #19128004 | 2 |
| #19127938 | 2 |
| #19127937 | 2 |
| #19127783 | 2 |
| C8×C22⋊D83 | 2 |
| #19127738 | 2 |
| C2×#107×C83 | 2 |
| #3339 | 83 |