Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #23782465 | C2 | semidirect |
| 2. #23782463 | C2 | semidirect |
| 3. #23781631 | C2 | semidirect |
| 4. C163⋊#338 | C2 | semidirect |
| 5. #408×C163 | C2 | semidirect |
| 92. C163 | #2017 | semidirect |
| 97. #408 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| #23782463 | 2 |
| #23781631 | 2 |
| C163⋊#338 | 2 |
| #408×C163 | 2 |
| #2017 | 163 |