Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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. #19128104 | C2 | semidirect |
| 3. #19128034 | C2 | semidirect |
| 4. #19128025 | C2 | semidirect |
| 5. #19127986 | C2 | semidirect |
| 6. #19127978 | C2 | semidirect |
| 7. #19127949 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127744 | C2 | semidirect |
| 11. #556×C83 | C2 | semidirect |
| 99. C83⋊C8 | #41 | semidirect |
| 123. C83 | #3353 | semidirect |
| 124. #556 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128355 | 2 |
| #19128104 | 2 |
| #19128034 | 2 |
| #19128025 | 2 |
| #19127986 | 2 |
| #19127978 | 2 |
| #19127949 | 2 |
| C4×#13050577 | 2 |
| #19127779 | 2 |
| #19127744 | 2 |
| #556×C83 | 2 |
| #3353 | 83 |