Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19127727 | C2 | semidirect |
| 3. #19127698 | C2 | semidirect |
| 4. #19127675 | C2 | semidirect |
| 5. #19127674 | C2 | semidirect |
| 6. #19127457 | C2 | semidirect |
| 7. #416×C83 | C2 | semidirect |
| 119. C83 | #2053 | semidirect |
| 123. #416 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128499 | 2 |
| #19127727 | 2 |
| #19127698 | 2 |
| #19127675 | 2 |
| #19127674 | 2 |
| #19127457 | 2 |
| #416×C83 | 2 |
| #2053 | 83 |