Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
218 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 31. Dic316 | C16 | direct (N × H) |
| 45. C16×C79 | Q16 | semidirect |
| 77. C79 | C16×Q16 | semidirect |
| 117. C16 | Dic316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic158 | 2 |
| C8×Dic316 | 2 |
| #23761470 | 2 |
| #23761380 | 2 |
| C8×C16×C79 | 2 |
| C16×Q16 | 79 |