Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
332 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 11. #14581790 | C4 | semidirect |
| 99. Dic83 | #103 | semidirect |
| 106. C83 | #1956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581790 | 2 |
| C2×#14581717 | 2 |
| C2×#14581716 | 2 |
| C2×#14581715 | 2 |
| C2×C8×Dic83 | 2 |
| #19127570 | 2 |
| C2×#103×C83 | 2 |
| #1956 | 83 |