Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D332 | C2 | semidirect |
| 2. #19128017 | C2 | semidirect |
| 3. #19127988 | C2 | semidirect |
| 4. #19127893 | C2 | semidirect |
| 5. #19127834 | C2 | semidirect |
| 6. #19127811 | C2 | semidirect |
| 7. #19127758 | C2 | semidirect |
| 8. #532×C83 | C2 | semidirect |
| 18. #14581723 | C22 | semidirect |
| 19. C4⋊(C83⋊C8) | C22 | semidirect |
| 20. #14581713 | C22 | semidirect |
| 23. #14581703 | C22 | semidirect |
| 25. C4⋊Q8×C83 | C22 | semidirect |
| 26. #127×C83 | C22 | semidirect |
| 31. C4×D4×C83 | C22 | semidirect |
| 91. D332 | #41 | semidirect |
| 121. C83 | #3109 | semidirect |
| 122. #532 | D83 | semidirect |
| 134. C4⋊Q8 | C2×D83 | semidirect |
| 135. #127 | C2×D83 | semidirect |
| 144. C4×D4 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D332 | 2 |
| #19128017 | 2 |
| #19127988 | 2 |
| #19127893 | 2 |
| #19127834 | 2 |
| #19127811 | 2 |
| #19127758 | 2 |
| #532×C83 | 2 |
| #3109 | 83 |