Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 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. #19127750 | C2 | semidirect |
| 4. #19127472 | C2 | semidirect |
| 5. #19127471 | C2 | semidirect |
| 6. #19127457 | C2 | semidirect |
| 86. C83 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127750 | 2 |
| #19127706 | 2 |
| C2×#14581709 | 2 |
| #19127472 | 2 |
| #19127471 | 2 |
| #19127457 | 2 |
| #418×C83 | 2 |
| #2081 | 83 |