Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 4. #19127607 | C2 | semidirect |
| 5. #19127607 | C2 | semidirect |
| 6. #19127586 | C2 | semidirect |
| 7. #19127571 | C2 | semidirect |
| 8. #19127567 | C2 | semidirect |
| 109. C83 | #2499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581771 | 2 |
| C2×#14581751 | 2 |
| #19127626 | 2 |
| #19127607 | 2 |
| #19127586 | 2 |
| #19127571 | 2 |
| #19127567 | 2 |
| C4×C22⋊C4×C83 | 2 |
| #2499 | 83 |