Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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. C2×#14581825 | C2 | semidirect |
| 2. C22×#13050579 | C2 | semidirect |
| 4. #19128178 | C2 | semidirect |
| 5. #19127924 | C2 | semidirect |
| 6. #19127902 | C2 | semidirect |
| 7. #19127707 | C2 | semidirect |
| 8. #19127698 | C2 | semidirect |
| 9. #424×C83 | C2 | semidirect |
| 14. C2×Dic332 | C22 | semidirect |
| 17. C2×#13050579 | C22 | semidirect |
| 22. C4×Dic166 | C22 | semidirect |
| 26. #14581717 | C22 | semidirect |
| 28. #14581714 | C22 | semidirect |
| 32. C4⋊C8×C83 | C22 | semidirect |
| 38. C2×Dic166 | D4 | semidirect |
| 117. C83 | #3043 | semidirect |
| 124. #424 | 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 |
|---|---|
| C2×#14581825 | 2 |
| C22×#13050579 | 2 |
| #19128270 | 2 |
| #19128178 | 2 |
| #19127924 | 2 |
| #19127902 | 2 |
| #19127707 | 2 |
| #19127698 | 2 |
| #424×C83 | 2 |
| #3043 | 83 |