Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #19127997 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 8. Q16×Dic83 | C2 | semidirect |
| 9. #19127793 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 104. C4×D83 | Q16 | semidirect |
| 133. C83 | #3104 | semidirect |
| 140. #462 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4×Q8×D83 | 2 |
| #19128035 | 2 |
| #19127997 | 2 |
| #19127996 | 2 |
| #19127908 | 2 |
| #19127855 | 2 |
| Q16×Dic83 | 2 |
| #19127793 | 2 |
| #19127753 | 2 |
| #462×C83 | 2 |
| #3104 | 83 |