Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
210 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 56. C8×C79 | Q32 | semidirect |
| 77. C79 | #12083 | semidirect |
| 129. C8 | Dic632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic632 | 2 |
| #23762298 | 2 |
| #23761472 | 2 |
| #23761365 | 2 |
| C8×C16×C79 | 2 |
| #12083 | 79 |