Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
552 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#14581719 | C2 | semidirect |
| 2. #19127702 | C2 | semidirect |
| 3. C2×#14581711 | C2 | semidirect |
| 4. #19127608 | C2 | semidirect |
| 16. 2−1+4×C83 | C4 | semidirect |
| 102. C83 | #1793 | semidirect |
| 110. 2−1+4 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581719 | 2 |
| #19127702 | 2 |
| C2×#14581711 | 2 |
| #19127608 | 2 |
| C2×2−1+4×C83 | 2 |
| #1793 | 83 |