Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #19128329 | C2 | semidirect |
| 5. #19127469 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 7. #339×C83 | C2 | semidirect |
| 32. C2×D332 | Q8 | semidirect |
| 113. C83 | #2027 | semidirect |
| 120. #339 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19127707 | 2 |
| #19127705 | 2 |
| #19127603 | 2 |
| #19127469 | 2 |
| #19127461 | 2 |
| #339×C83 | 2 |
| #2027 | 83 |