Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#14581717 | C2 | semidirect |
| 4. #19127464 | C2 | semidirect |
| 8. #14581771 | C4 | semidirect |
| 96. C83 | #1894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581771 | 2 |
| C2×#14581717 | 2 |
| #19127561 | 2 |
| #19127464 | 2 |
| C22×M16×C83 | 2 |
| #1894 | 83 |