Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23782140 | C2 | semidirect |
| 2. #23781670 | C2 | semidirect |
| 3. C2×#19104652 | C2 | semidirect |
| 4. #23781425 | C2 | semidirect |
| 16. #127×C163 | C4 | semidirect |
| 22. C4⋊Dic163 | D4 | semidirect |
| 36. C2×D4×C163 | C2×C4 | semidirect |
| 41. C42×C163 | C2×C4 | semidirect |
| 87. C163 | #1887 | semidirect |
| 99. #127 | Dic163 | semidirect |
| 116. C2×D4 | C2×Dic163 | semidirect |
| 129. C42 | C2×Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782140 | 2 |
| #23781670 | 2 |
| C2×#19104652 | 2 |
| #23781425 | 2 |
| C2×#127×C163 | 2 |
| #1887 | 163 |