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. #23781977 | C2 | semidirect |
| 4. #23781961 | C2 | semidirect |
| 5. #23781960 | C2 | semidirect |
| 6. #23781862 | C2 | semidirect |
| 7. #23781802 | C2 | semidirect |
| 8. #23781766 | C2 | semidirect |
| 9. #23781762 | C2 | semidirect |
| 10. #23781721 | C2 | semidirect |
| 11. #460×C163 | C2 | semidirect |
| 87. Dic326 | #41 | semidirect |
| 105. Q8×C163 | #41 | semidirect |
| 140. C163 | #3112 | semidirect |
| 148. #460 | D163 | semidirect |
| 231. Q8 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782213 | 2 |
| C4×Q8×D163 | 2 |
| #23781977 | 2 |
| #23781961 | 2 |
| #23781960 | 2 |
| #23781862 | 2 |
| #23781802 | 2 |
| #23781766 | 2 |
| #23781762 | 2 |
| #23781721 | 2 |
| #460×C163 | 2 |
| #3112 | 163 |