Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4×Q8×D83 | C2 | semidirect |
| 3. #19128016 | C2 | semidirect |
| 4. #19127993 | C2 | semidirect |
| 5. #19127902 | C2 | semidirect |
| 6. #19127901 | C2 | semidirect |
| 7. #19127841 | C2 | semidirect |
| 8. #19127804 | C2 | semidirect |
| 9. #19127800 | C2 | semidirect |
| 10. #19127757 | C2 | semidirect |
| 11. #477×C83 | C2 | semidirect |
| 87. Q8×C83 | #41 | semidirect |
| 113. Dic166 | #41 | semidirect |
| 141. C83 | #3112 | semidirect |
| 146. #477 | D83 | semidirect |
| 231. Q8 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| C4×Q8×D83 | 2 |
| #19128016 | 2 |
| #19127993 | 2 |
| #19127902 | 2 |
| #19127901 | 2 |
| #19127841 | 2 |
| #19127804 | 2 |
| #19127800 | 2 |
| #19127757 | 2 |
| #477×C83 | 2 |
| #3112 | 83 |