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. C2×#14581817 | C2 | semidirect |
| 2. C2×#14581817 | C2 | semidirect |
| 3. #19128468 | C2 | semidirect |
| 4. #19127969 | C2 | semidirect |
| 5. #19127966 | C2 | semidirect |
| 6. #19127749 | C2 | semidirect |
| 7. #19127685 | C2 | semidirect |
| 8. C2×#14581708 | C2 | semidirect |
| 9. #575×C83 | C2 | semidirect |
| 16. C2×#13050577 | C22 | semidirect |
| 18. C2×#13050575 | C22 | semidirect |
| 20. #14581799 | C22 | semidirect |
| 25. #14581727 | C22 | semidirect |
| 26. #14581711 | C22 | semidirect |
| 27. #14581709 | C22 | semidirect |
| 28. #14581708 | C22 | semidirect |
| 32. #137×C83 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C83 | C22 | semidirect |
| 148. C83 | #3068 | semidirect |
| 149. #575 | D83 | semidirect |
| 162. #137 | C2×D83 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581817 | 2 |
| #19128468 | 2 |
| #19127969 | 2 |
| #19127966 | 2 |
| #19127749 | 2 |
| #19127685 | 2 |
| C2×#14581708 | 2 |
| #575×C83 | 2 |
| #3068 | 83 |