Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128095 | C2 | semidirect |
| 4. #19128061 | C2 | semidirect |
| 5. #19127924 | C2 | semidirect |
| 6. #19127859 | C2 | semidirect |
| 8. #432×C83 | C2 | semidirect |
| 11. C2×Dic332 | C22 | semidirect |
| 13. #14581792 | C22 | semidirect |
| 14. #14581792 | C22 | semidirect |
| 23. C4×Dic166 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 30. C4⋊C8×C83 | C22 | semidirect |
| 32. #97×C83 | C22 | semidirect |
| 113. C83 | #3215 | semidirect |
| 121. #432 | D83 | semidirect |
| 141. C4⋊C8 | C2×D83 | semidirect |
| 145. #97 | 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×#14581780 | 2 |
| #19128095 | 2 |
| #19128061 | 2 |
| #19127924 | 2 |
| #19127859 | 2 |
| #19127854 | 2 |
| #432×C83 | 2 |
| #3215 | 83 |