Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #19127750 | C2 | semidirect |
| 3. #19127749 | C2 | semidirect |
| 6. #19127466 | C2 | semidirect |
| 7. #341×C83 | C2 | semidirect |
| 92. C83 | #1858 | semidirect |
| 99. #341 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128467 | 2 |
| #19127750 | 2 |
| #19127749 | 2 |
| #19127683 | 2 |
| #19127667 | 2 |
| #19127466 | 2 |
| #341×C83 | 2 |
| #1858 | 83 |