Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #19128100 | C2 | semidirect |
| 4. #19128080 | C2 | semidirect |
| 5. #19128070 | C2 | semidirect |
| 8. #19127805 | C2 | semidirect |
| 9. #19127793 | C2 | semidirect |
| 11. #491×C83 | C2 | semidirect |
| 103. C83 | #3177 | semidirect |
| 109. #491 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128314 | 2 |
| #19128312 | 2 |
| #19128100 | 2 |
| #19128080 | 2 |
| #19128070 | 2 |
| #19127958 | 2 |
| #19127941 | 2 |
| #19127805 | 2 |
| #19127793 | 2 |
| #19127658 | 2 |
| #491×C83 | 2 |
| #3177 | 83 |