Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782375 | C2 | semidirect |
| 2. #23782019 | C2 | semidirect |
| 3. #23782015 | C2 | semidirect |
| 4. #23781972 | C2 | semidirect |
| 5. #23781955 | C2 | semidirect |
| 7. #23781867 | C2 | semidirect |
| 8. Q8×C163⋊C8 | C2 | semidirect |
| 9. C4×#14579686 | C2 | semidirect |
| 11. #556×C163 | C2 | semidirect |
| 120. C163 | #3360 | semidirect |
| 122. #556 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782375 | 2 |
| #23782019 | 2 |
| #23782015 | 2 |
| #23781972 | 2 |
| #23781955 | 2 |
| #23781877 | 2 |
| #23781867 | 2 |
| Q8×C163⋊C8 | 2 |
| C4×#14579686 | 2 |
| C4×#14579684 | 2 |
| #556×C163 | 2 |
| #3360 | 163 |