Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #19128516 | C2 | semidirect |
| 2. #19128515 | C2 | semidirect |
| 3. #19128079 | C2 | semidirect |
| 4. #19127976 | C2 | semidirect |
| 5. #19127974 | C2 | semidirect |
| 6. #19127973 | C2 | semidirect |
| 7. #19127884 | C2 | semidirect |
| 8. #19127882 | C2 | semidirect |
| 9. #19127818 | C2 | semidirect |
| 10. #19127816 | C2 | semidirect |
| 11. #578×C83 | C2 | semidirect |
| 147. C83 | #3293 | semidirect |
| 150. #578 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128516 | 2 |
| #19128515 | 2 |
| #19128079 | 2 |
| #19127976 | 2 |
| #19127974 | 2 |
| #19127973 | 2 |
| #19127884 | 2 |
| #19127882 | 2 |
| #19127818 | 2 |
| #19127816 | 2 |
| #578×C83 | 2 |
| #3293 | 83 |