Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #19127749 | C2 | semidirect |
| 4. C4×#13050574 | C2 | semidirect |
| 5. #19127472 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 14. #14581711 | C4 | semidirect |
| 15. #14581709 | C4 | semidirect |
| 96. C83 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127749 | 2 |
| #19127718 | 2 |
| #19127685 | 2 |
| C4×#13050574 | 2 |
| #19127472 | 2 |
| #19127461 | 2 |
| C2×#104×C83 | 2 |
| #1932 | 83 |