Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 3. #19128104 | C2 | semidirect |
| 4. #19128038 | C2 | semidirect |
| 5. #19128035 | C2 | semidirect |
| 6. #19127997 | C2 | semidirect |
| 7. #19127941 | C2 | semidirect |
| 8. C4×#13050580 | C2 | semidirect |
| 10. #107×D83 | C2 | semidirect |
| 11. #477×C83 | C2 | semidirect |
| 87. D332 | Q16 | semidirect |
| 118. C83 | #3338 | semidirect |
| 125. #477 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128412 | 2 |
| #19128411 | 2 |
| #19128104 | 2 |
| #19128038 | 2 |
| #19128035 | 2 |
| #19127997 | 2 |
| #19127941 | 2 |
| C4×#13050580 | 2 |
| #19127766 | 2 |
| #107×D83 | 2 |
| #477×C83 | 2 |
| #3338 | 83 |