Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 85. C2×C4×C163 | Q16 | semidirect |
| 116. C163 | #2056 | semidirect |
| 200. C2×C4 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| C2×C4⋊(C163⋊C8) | 2 |
| C2×#19104659 | 2 |
| C2×#19104658 | 2 |
| #23781571 | 2 |
| #23781427 | 2 |
| #391×C163 | 2 |
| #2056 | 163 |