Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#14581784 | C2 | semidirect |
| 2. #19128100 | C2 | semidirect |
| 3. #19128055 | C2 | semidirect |
| 4. #19128034 | C2 | semidirect |
| 5. #19128029 | C2 | semidirect |
| 8. #19128008 | C2 | semidirect |
| 9. #19128001 | C2 | semidirect |
| 10. #19127754 | C2 | semidirect |
| 126. C83 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581784 | 2 |
| #19128100 | 2 |
| #19128055 | 2 |
| #19128034 | 2 |
| #19128029 | 2 |
| #19128017 | 2 |
| #19128012 | 2 |
| #19128008 | 2 |
| #19128001 | 2 |
| #19127754 | 2 |
| #529×C83 | 2 |
| #3232 | 83 |