Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 45. C163⋊C8 | Q16 | semidirect |
| 70. C163 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782061 | 2 |
| #23781960 | 2 |
| #23781796 | 2 |
| #23781417 | 2 |
| #23781413 | 2 |
| #23781411 | 2 |
| #462×C163 | 2 |
| #1692 | 163 |