Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19127659 | C2 | semidirect |
| 4. C2×#14581703 | C2 | semidirect |
| 5. #19127465 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 9. #14581799 | C4 | semidirect |
| 16. #14581716 | C4 | semidirect |
| 17. #14581713 | C4 | semidirect |
| 24. #104×C83 | C4 | semidirect |
| 99. C83 | #1765 | semidirect |
| 118. #104 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581799 | 2 |
| #19127697 | 2 |
| #19127659 | 2 |
| C2×#14581703 | 2 |
| #19127465 | 2 |
| #19127461 | 2 |
| C2×#104×C83 | 2 |
| #1765 | 83 |