Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 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. #19128047 | C2 | semidirect |
| 2. #19127907 | C2 | semidirect |
| 4. #19127778 | C2 | semidirect |
| 5. #19127451 | C2 | semidirect |
| 6. #19127446 | C2 | semidirect |
| 7. #331×C83 | C2 | semidirect |
| 85. C83 | #1701 | semidirect |
| 92. #331 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128047 | 2 |
| #19127907 | 2 |
| #19127893 | 2 |
| #19127778 | 2 |
| #19127451 | 2 |
| #19127446 | 2 |
| #331×C83 | 2 |
| #1701 | 83 |