Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19128049 | C2 | semidirect |
| 3. #19128014 | C2 | semidirect |
| 4. #19127993 | C2 | semidirect |
| 5. #19127949 | C2 | semidirect |
| 6. #19127901 | C2 | semidirect |
| 7. #19127861 | C2 | semidirect |
| 8. C4×#13050580 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127700 | C2 | semidirect |
| 11. #554×C83 | C2 | semidirect |
| 129. C83 | #3333 | semidirect |
| 130. #554 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128372 | 2 |
| #19128049 | 2 |
| #19128014 | 2 |
| #19127993 | 2 |
| #19127949 | 2 |
| #19127901 | 2 |
| #19127861 | 2 |
| C4×#13050580 | 2 |
| #19127779 | 2 |
| #19127700 | 2 |
| #554×C83 | 2 |
| #3333 | 83 |