Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128329 | C2 | semidirect |
| 2. #19128069 | C2 | semidirect |
| 3. #19128060 | C2 | semidirect |
| 4. #19128055 | C2 | semidirect |
| 5. #19128051 | C2 | semidirect |
| 6. #19127710 | C2 | semidirect |
| 9. C2×#14581716 | C2 | semidirect |
| 10. #19127657 | C2 | semidirect |
| 128. C83 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128069 | 2 |
| #19128060 | 2 |
| #19128055 | 2 |
| #19128051 | 2 |
| #19127710 | 2 |
| #19127702 | 2 |
| #19127697 | 2 |
| C2×#14581716 | 2 |
| #19127657 | 2 |
| #536×C83 | 2 |
| #3137 | 83 |