Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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. #19127809 | C2 | semidirect |
| 4. #19127524 | C2 | semidirect |
| 5. #19127518 | C2 | semidirect |
| 7. #347×C83 | C2 | semidirect |
| 12. Dic664 | C4 | semidirect |
| 13. #14581737 | C4 | semidirect |
| 65. C83 | #2180 | semidirect |
| 72. #347 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128144 | 2 |
| #19127824 | 2 |
| #19127809 | 2 |
| #19127524 | 2 |
| #19127518 | 2 |
| #19127512 | 2 |
| #347×C83 | 2 |
| #2180 | 83 |