Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4⋊Q8×D163 | C2 | semidirect |
| 3. #23782027 | C2 | semidirect |
| 4. #23782025 | C2 | semidirect |
| 5. #23782024 | C2 | semidirect |
| 6. #23782014 | C2 | semidirect |
| 7. #23782010 | C2 | semidirect |
| 8. #23781665 | C2 | semidirect |
| 9. #23781663 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #489×C163 | C2 | semidirect |
| 140. C163 | #3141 | semidirect |
| 147. #489 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782214 | 2 |
| C4⋊Q8×D163 | 2 |
| #23782027 | 2 |
| #23782025 | 2 |
| #23782024 | 2 |
| #23782014 | 2 |
| #23782010 | 2 |
| #23781665 | 2 |
| #23781663 | 2 |
| #23781617 | 2 |
| #489×C163 | 2 |
| #3141 | 163 |