Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128071 | C2 | semidirect |
| 3. #19128063 | C2 | semidirect |
| 4. #19128058 | C2 | semidirect |
| 5. #19128053 | C2 | semidirect |
| 6. #19127709 | C2 | semidirect |
| 9. C2×#14581715 | C2 | semidirect |
| 10. #19127657 | C2 | semidirect |
| 11. #544×C83 | C2 | semidirect |
| 128. C83 | #3137 | semidirect |
| 129. #544 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128277 | 2 |
| #19128071 | 2 |
| #19128063 | 2 |
| #19128058 | 2 |
| #19128053 | 2 |
| #19127709 | 2 |
| #19127700 | 2 |
| #19127695 | 2 |
| C2×#14581715 | 2 |
| #19127657 | 2 |
| #544×C83 | 2 |
| #3137 | 83 |