Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128066 | C2 | semidirect |
| 4. #19128061 | C2 | semidirect |
| 5. #19128056 | C2 | semidirect |
| 6. #19128048 | C2 | semidirect |
| 7. #19127707 | C2 | semidirect |
| 8. #19127703 | C2 | semidirect |
| 9. #19127698 | C2 | semidirect |
| 10. C2×#14581714 | C2 | semidirect |
| 11. #405×C83 | C2 | semidirect |
| 14. #14581792 | C22 | semidirect |
| 17. #14581784 | C22 | semidirect |
| 26. #14581717 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 28. #14581717 | C22 | semidirect |
| 33. #14581714 | C22 | semidirect |
| 34. #14581714 | C22 | semidirect |
| 35. #14581714 | C22 | semidirect |
| 39. #97×C83 | C22 | semidirect |
| 40. C4×C8×C83 | C22 | semidirect |
| 136. C83 | #3136 | semidirect |
| 147. #405 | D83 | semidirect |
| 175. #97 | C2×D83 | semidirect |
| 176. 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 |
| #19128270 | 2 |
| #19128066 | 2 |
| #19128061 | 2 |
| #19128056 | 2 |
| #19128048 | 2 |
| #19127707 | 2 |
| #19127703 | 2 |
| #19127698 | 2 |
| C2×#14581714 | 2 |
| #405×C83 | 2 |
| #3136 | 83 |