Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. #19127748 | C2 | semidirect |
| 3. #19127525 | C2 | semidirect |
| 4. #19127524 | C2 | semidirect |
| 5. #19127514 | C2 | semidirect |
| 6. #19127482 | C2 | semidirect |
| 7. #361×C83 | C2 | semidirect |
| 66. C83 | #2238 | semidirect |
| 72. #361 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127951 | 2 |
| #19127748 | 2 |
| #19127525 | 2 |
| #19127524 | 2 |
| #19127514 | 2 |
| #19127482 | 2 |
| #361×C83 | 2 |
| #2238 | 83 |