Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #19128355 | C2 | semidirect |
| 2. #19128047 | C2 | semidirect |
| 3. #19128017 | C2 | semidirect |
| 4. #19127986 | C2 | semidirect |
| 5. #19127952 | C2 | semidirect |
| 6. #19127893 | C2 | semidirect |
| 7. #19127846 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127702 | C2 | semidirect |
| 11. #550×C83 | C2 | semidirect |
| 81. Q8×C83 | #41 | semidirect |
| 135. C83 | #3332 | semidirect |
| 136. #550 | D83 | semidirect |
| 217. Q8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128355 | 2 |
| #19128047 | 2 |
| #19128017 | 2 |
| #19127986 | 2 |
| #19127952 | 2 |
| #19127893 | 2 |
| #19127846 | 2 |
| C4×#13050577 | 2 |
| #19127779 | 2 |
| #19127702 | 2 |
| #550×C83 | 2 |
| #3332 | 83 |