Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. #19128499 | C2 | semidirect |
| 2. C2×#14581818 | C2 | semidirect |
| 3. #19128468 | C2 | semidirect |
| 4. #19127969 | C2 | semidirect |
| 5. #19127962 | C2 | semidirect |
| 6. #19127749 | C2 | semidirect |
| 7. #19127683 | C2 | semidirect |
| 8. C2×#14581709 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C83 | C2 | semidirect |
| 12. #14581822 | C22 | semidirect |
| 16. #14581817 | C22 | semidirect |
| 18. C2×#13050578 | C22 | semidirect |
| 19. C2×#13050575 | C22 | semidirect |
| 21. #14581799 | C22 | semidirect |
| 26. #14581727 | C22 | semidirect |
| 27. #14581710 | C22 | semidirect |
| 28. #14581709 | C22 | semidirect |
| 29. #14581708 | C22 | semidirect |
| 148. C83 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128499 | 2 |
| C2×#14581818 | 2 |
| #19128468 | 2 |
| #19127969 | 2 |
| #19127962 | 2 |
| #19127749 | 2 |
| #19127683 | 2 |
| C2×#14581709 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #3068 | 83 |