Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13050575 | C2 | semidirect |
| 2. #19128265 | C2 | semidirect |
| 3. #19128176 | C2 | semidirect |
| 4. #19127918 | C2 | semidirect |
| 5. #19127894 | C2 | semidirect |
| 6. #19127729 | C2 | semidirect |
| 7. #19127707 | C2 | semidirect |
| 8. #19127697 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C83 | C2 | semidirect |
| 14. #14581788 | C22 | semidirect |
| 15. #14581781 | C22 | semidirect |
| 19. D4×Dic83 | C22 | semidirect |
| 23. Dic83⋊C8 | C22 | semidirect |
| 24. #14581716 | C22 | semidirect |
| 25. #14581714 | C22 | semidirect |
| 26. #14581713 | C22 | semidirect |
| 30. C2×SD16×C83 | C22 | semidirect |
| 31. C2×D8×C83 | C22 | semidirect |
| 58. C2×D4×C83 | D4 | semidirect |
| 122. C83 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D83 | semidirect |
| 136. C2×SD16 | C2×D83 | semidirect |
| 139. C2×D8 | C2×D83 | semidirect |
| 168. C2×D4 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050575 | 2 |
| #19128265 | 2 |
| #19128176 | 2 |
| #19127918 | 2 |
| #19127894 | 2 |
| #19127729 | 2 |
| #19127707 | 2 |
| #19127697 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #3041 | 83 |