Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #19128043 | C2 | semidirect |
| 4. #19128037 | C2 | semidirect |
| 5. #19128032 | C2 | semidirect |
| 6. #19127743 | C2 | semidirect |
| 7. #19127711 | C2 | semidirect |
| 25. #14581726 | C22 | semidirect |
| 26. #14581724 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 28. #14581717 | C22 | semidirect |
| 117. C83 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581771 | 2 |
| C2×#14581751 | 2 |
| #19128043 | 2 |
| #19128037 | 2 |
| #19128032 | 2 |
| #19127743 | 2 |
| #19127711 | 2 |
| #407×C83 | 2 |
| #3095 | 83 |