Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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. #19127600 | C2 | semidirect |
| 3. #19127567 | C2 | semidirect |
| 5. C4⋊C4×Dic83 | C2 | semidirect |
| 7. #19127547 | C2 | semidirect |
| 21. #117×C83 | C4 | semidirect |
| 95. C83 | #2346 | semidirect |
| 105. #117 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127600 | 2 |
| #19127594 | 2 |
| #19127567 | 2 |
| #19127561 | 2 |
| C4⋊C4×Dic83 | 2 |
| C4×C22⋊Dic83 | 2 |
| #19127547 | 2 |
| C2×#117×C83 | 2 |
| #2346 | 83 |