Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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. #19127525 | C2 | semidirect |
| 6. #14581732 | C4 | semidirect |
| 8. C2×C83⋊C16 | C4 | semidirect |
| 56. C83 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581732 | 2 |
| #19127739 | 2 |
| #19127525 | 2 |
| C2×#108×C83 | 2 |
| #2155 | 83 |