Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19127819 | C2 | semidirect |
| 3. #19127530 | C2 | semidirect |
| 4. #19127508 | C2 | semidirect |
| 5. #19127507 | C2 | semidirect |
| 6. C4×C83⋊C16 | C2 | semidirect |
| 7. #443×C83 | C2 | semidirect |
| 10. #14581738 | C4 | semidirect |
| 11. #14581736 | C4 | semidirect |
| 12. #14581735 | C4 | semidirect |
| 13. #14581733 | C4 | semidirect |
| 72. C83 | #2178 | semidirect |
| 75. #443 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128131 | 2 |
| #19127819 | 2 |
| #19127530 | 2 |
| #19127508 | 2 |
| #19127507 | 2 |
| C4×C83⋊C16 | 2 |
| #443×C83 | 2 |
| #2178 | 83 |