Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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. C2×#14581823 | C2 | semidirect |
| 2. C22×#13050577 | C2 | semidirect |
| 4. #19127923 | C2 | semidirect |
| 5. #19127901 | C2 | semidirect |
| 6. #19127728 | C2 | semidirect |
| 7. #19127705 | C2 | semidirect |
| 8. #19127695 | C2 | semidirect |
| 9. #519×C83 | C2 | semidirect |
| 13. C2×#13050580 | C22 | semidirect |
| 16. C2×#13050577 | C22 | semidirect |
| 23. C4⋊(C83⋊C8) | C22 | semidirect |
| 24. #14581715 | C22 | semidirect |
| 26. #14581712 | C22 | semidirect |
| 29. C4×Q8×C83 | C22 | semidirect |
| 55. C2×Q8×C83 | D4 | semidirect |
| 117. C83 | #3043 | semidirect |
| 121. #519 | D83 | semidirect |
| 142. C4×Q8 | C2×D83 | semidirect |
| 156. C2×Q8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| C22×#13050577 | 2 |
| #19128270 | 2 |
| #19127923 | 2 |
| #19127901 | 2 |
| #19127728 | 2 |
| #19127705 | 2 |
| #19127695 | 2 |
| #519×C83 | 2 |
| #3043 | 83 |