Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128045 | C2 | semidirect |
| 5. #19128040 | C2 | semidirect |
| 6. #19127987 | C2 | semidirect |
| 7. #19127941 | C2 | semidirect |
| 8. C4×#13050580 | C2 | semidirect |
| 10. #19127736 | C2 | semidirect |
| 11. #475×C83 | C2 | semidirect |
| 116. C83 | #3342 | semidirect |
| 123. #475 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128425 | 2 |
| #19128424 | 2 |
| #19128104 | 2 |
| #19128045 | 2 |
| #19128040 | 2 |
| #19127987 | 2 |
| #19127941 | 2 |
| C4×#13050580 | 2 |
| #19127766 | 2 |
| #19127736 | 2 |
| #475×C83 | 2 |
| #3342 | 83 |