Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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. C2×#14581811 | C2 | semidirect |
| 2. C22×Dic332 | C2 | semidirect |
| 3. #19128357 | C2 | semidirect |
| 4. #19128084 | C2 | semidirect |
| 5. #19127943 | C2 | semidirect |
| 6. #19127922 | C2 | semidirect |
| 7. #19127864 | C2 | semidirect |
| 8. #19127839 | C2 | semidirect |
| 9. #19127795 | C2 | semidirect |
| 10. C8×C22⋊D83 | C2 | semidirect |
| 11. #466×C83 | C2 | semidirect |
| 55. Dic332 | D4 | semidirect |
| 116. C22×C83 | #135 | semidirect |
| 137. C83 | #3285 | semidirect |
| 143. #466 | D83 | semidirect |
| 256. C22 | #14581811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581811 | 2 |
| C22×Dic332 | 2 |
| #19128357 | 2 |
| #19128084 | 2 |
| #19127943 | 2 |
| #19127922 | 2 |
| #19127864 | 2 |
| #19127839 | 2 |
| #19127795 | 2 |
| C8×C22⋊D83 | 2 |
| #466×C83 | 2 |
| #3285 | 83 |