Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#14581799 | C2 | semidirect |
| 2. #19127823 | C2 | semidirect |
| 3. #19127818 | C2 | semidirect |
| 4. #19127750 | C2 | semidirect |
| 5. #19127718 | C2 | semidirect |
| 6. #19127659 | C2 | semidirect |
| 10. #14581799 | C22 | semidirect |
| 11. #14581799 | C22 | semidirect |
| 17. #14581728 | C22 | semidirect |
| 18. #14581719 | C22 | semidirect |
| 19. #14581702 | C22 | semidirect |
| 20. C8×Dic83 | C22 | semidirect |
| 22. #137×C83 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C83 | C4 | semidirect |
| 90. C83 | #2955 | semidirect |
| 99. #137 | Dic83 | semidirect |
| 100. AGL(1,ℤ/8) | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581799 | 2 |
| #19127823 | 2 |
| #19127818 | 2 |
| #19127750 | 2 |
| #19127718 | 2 |
| #19127659 | 2 |
| #575×C83 | 2 |
| #2955 | 83 |