Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #19127993 | C2 | semidirect |
| 5. Q8⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127431 | C2 | semidirect |
| 7. #477×C83 | C2 | semidirect |
| 90. C83 | #1630 | semidirect |
| 94. #477 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128436 | 2 |
| #19128075 | 2 |
| #19127993 | 2 |
| #19127444 | 2 |
| Q8⋊(C83⋊C8) | 2 |
| #19127431 | 2 |
| #477×C83 | 2 |
| #1630 | 83 |