Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23782044 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23782012 | C2 | semidirect |
| 5. #23782011 | C2 | semidirect |
| 6. C8×C163⋊C8 | C2 | semidirect |
| 7. #486×C163 | C2 | semidirect |
| 74. C163 | #1709 | semidirect |
| 81. #486 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782044 | 2 |
| #23782041 | 2 |
| #23782013 | 2 |
| #23782012 | 2 |
| #23782011 | 2 |
| C8×C163⋊C8 | 2 |
| #486×C163 | 2 |
| #1709 | 163 |