Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19128329 | C2 | semidirect |
| 3. #19128002 | C2 | semidirect |
| 4. #19128002 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127982 | C2 | semidirect |
| 7. #19127743 | C2 | semidirect |
| 8. #19127739 | C2 | semidirect |
| 11. #424×C83 | C2 | semidirect |
| 13. #14581792 | C22 | semidirect |
| 15. #14581784 | C22 | semidirect |
| 26. #14581726 | C22 | semidirect |
| 27. #14581726 | C22 | semidirect |
| 28. #14581726 | C22 | semidirect |
| 29. #14581724 | C22 | semidirect |
| 30. #14581724 | C22 | semidirect |
| 31. #14581724 | C22 | semidirect |
| 39. C4⋊C8×C83 | C22 | semidirect |
| 40. C4⋊C8×C83 | C22 | semidirect |
| 45. C2×D332 | Q8 | semidirect |
| 125. C83 | #3081 | semidirect |
| 134. #424 | D83 | semidirect |
| 160. C4⋊C8 | C2×D83 | semidirect |
| 161. C4⋊C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128175 | 2 |
| #19128002 | 2 |
| #19127992 | 2 |
| #19127982 | 2 |
| #19127743 | 2 |
| #19127739 | 2 |
| #19127707 | 2 |
| C2×#14581714 | 2 |
| #424×C83 | 2 |
| #3081 | 83 |