Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #19128258 | C2 | semidirect |
| 3. #19128002 | C2 | semidirect |
| 4. #19127992 | C2 | semidirect |
| 5. #19127982 | C2 | semidirect |
| 6. #19127743 | C2 | semidirect |
| 8. #423×C83 | C2 | semidirect |
| 11. #14581792 | C22 | semidirect |
| 12. #14581792 | C22 | semidirect |
| 13. #14581784 | C22 | semidirect |
| 25. #14581726 | C22 | semidirect |
| 26. #14581724 | C22 | semidirect |
| 31. C4⋊C8×C83 | C22 | semidirect |
| 32. C4⋊C8×C83 | C22 | semidirect |
| 38. C2×D332 | Q8 | semidirect |
| 116. C83 | #3077 | semidirect |
| 123. #423 | D83 | semidirect |
| 145. C4⋊C8 | C2×D83 | semidirect |
| 146. C4⋊C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| C2×C4×D332 | 2 |
| #19128002 | 2 |
| #19127992 | 2 |
| #19127982 | 2 |
| #19127743 | 2 |
| #19127707 | 2 |
| #423×C83 | 2 |
| #3077 | 83 |