Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. #19128251 | C2 | semidirect |
| 2. C2×C4×D332 | C2 | semidirect |
| 3. #19128015 | C2 | semidirect |
| 4. #19127982 | C2 | semidirect |
| 5. #19127897 | C2 | semidirect |
| 6. #19127837 | C2 | semidirect |
| 7. C4×D664 | C2 | semidirect |
| 8. #431×C83 | C2 | semidirect |
| 13. #14581792 | C22 | semidirect |
| 14. #14581789 | C22 | semidirect |
| 23. C4×D332 | C22 | semidirect |
| 26. #14581726 | C22 | semidirect |
| 28. #14581714 | C22 | semidirect |
| 30. C4⋊C8×C83 | C22 | semidirect |
| 32. C4×C8×C83 | C22 | semidirect |
| 73. C2×C4×C83 | D8 | semidirect |
| 89. D332 | #41 | semidirect |
| 121. C83 | #3100 | semidirect |
| 129. #431 | D83 | semidirect |
| 149. C4⋊C8 | C2×D83 | semidirect |
| 153. C4×C8 | C2×D83 | semidirect |
| 208. C2×C4 | D664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| C2×C4×D332 | 2 |
| #19128015 | 2 |
| #19127982 | 2 |
| #19127897 | 2 |
| #19127837 | 2 |
| C4×D664 | 2 |
| #431×C83 | 2 |
| #3100 | 83 |