Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782006 | C2 | semidirect |
| 3. #23782000 | C2 | semidirect |
| 4. #23781989 | C2 | semidirect |
| 5. #23781978 | C2 | semidirect |
| 6. #23781708 | C2 | semidirect |
| 7. C2×#19104668 | C2 | semidirect |
| 8. #23781664 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. #23781632 | C2 | semidirect |
| 11. #520×C163 | C2 | semidirect |
| 133. C163 | #3098 | semidirect |
| 136. #520 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782243 | 2 |
| #23782006 | 2 |
| #23782000 | 2 |
| #23781989 | 2 |
| #23781978 | 2 |
| #23781708 | 2 |
| C2×#19104668 | 2 |
| #23781664 | 2 |
| #23781659 | 2 |
| #23781632 | 2 |
| #520×C163 | 2 |
| #3098 | 163 |