Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#14581783 | C2 | semidirect |
| 3. #19128108 | C2 | semidirect |
| 4. #19128064 | C2 | semidirect |
| 5. #19128019 | C2 | semidirect |
| 6. #19128015 | C2 | semidirect |
| 7. #19128012 | C2 | semidirect |
| 8. #19128000 | C2 | semidirect |
| 9. #19127999 | C2 | semidirect |
| 10. #19127755 | C2 | semidirect |
| 11. #481×C83 | C2 | semidirect |
| 135. C83 | #3234 | semidirect |
| 141. #481 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128246 | 2 |
| C2×#14581783 | 2 |
| #19128108 | 2 |
| #19128064 | 2 |
| #19128019 | 2 |
| #19128015 | 2 |
| #19128012 | 2 |
| #19128000 | 2 |
| #19127999 | 2 |
| #19127755 | 2 |
| #481×C83 | 2 |
| #3234 | 83 |