Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128102 | C2 | semidirect |
| 3. #19128079 | C2 | semidirect |
| 4. #19128068 | C2 | semidirect |
| 7. #19127805 | C2 | semidirect |
| 8. Q16×Dic83 | C2 | semidirect |
| 9. #19127795 | C2 | semidirect |
| 112. C83 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128311 | 2 |
| #19128102 | 2 |
| #19128079 | 2 |
| #19128068 | 2 |
| #19127957 | 2 |
| #19127942 | 2 |
| #19127805 | 2 |
| Q16×Dic83 | 2 |
| #19127795 | 2 |
| #19127656 | 2 |
| #467×C83 | 2 |
| #3177 | 83 |