Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23781682 | C2 | semidirect |
| 2. #23781661 | C2 | semidirect |
| 3. #23781639 | C2 | semidirect |
| 4. #23781632 | C2 | semidirect |
| 6. C2×#14579683 | C22 | semidirect |
| 7. C22×C163⋊C8 | C22 | semidirect |
| 8. #19104694 | C22 | semidirect |
| 15. 2−1+4×C163 | C4 | semidirect |
| 18. H(5,𝔽2)×C163 | C4 | semidirect |
| 108. C163 | #1794 | semidirect |
| 116. 2−1+4 | Dic163 | semidirect |
| 119. H(5,𝔽2) | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781682 | 2 |
| #23781661 | 2 |
| #23781639 | 2 |
| #23781632 | 2 |
| #585×C163 | 2 |
| #1794 | 163 |