Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×D664 | C2 | semidirect |
| 2. #19128265 | C2 | semidirect |
| 3. #19127954 | C2 | semidirect |
| 4. #19127937 | C2 | semidirect |
| 5. #19127739 | C2 | semidirect |
| 6. #19127707 | C2 | semidirect |
| 7. C2×#131×C83 | C2 | semidirect |
| 14. #14581766 | C22 | semidirect |
| 17. #14581726 | C22 | semidirect |
| 18. #14581724 | C22 | semidirect |
| 19. #14581714 | C22 | semidirect |
| 23. C2×M16×C83 | C22 | semidirect |
| 25. C22×C8×C83 | C22 | semidirect |
| 48. C2×C8×C83 | D4 | semidirect |
| 94. C83 | #3058 | semidirect |
| 96. C2×#131 | D83 | semidirect |
| 109. C2×M16 | C2×D83 | semidirect |
| 111. C22×C8 | C2×D83 | semidirect |
| 138. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| #19128265 | 2 |
| #19127954 | 2 |
| #19127937 | 2 |
| #19127739 | 2 |
| #19127707 | 2 |
| C2×#131×C83 | 2 |
| #3058 | 83 |