Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104768 | C2 | semidirect |
| 3. C22×#14579689 | C2 | semidirect |
| 4. #23782239 | C2 | semidirect |
| 5. #23782236 | C2 | semidirect |
| 6. #23782058 | C2 | semidirect |
| 7. #23782056 | C2 | semidirect |
| 8. #23782046 | C2 | semidirect |
| 9. #23782043 | C2 | semidirect |
| 10. #23781623 | C2 | semidirect |
| 11. C2×#137×C163 | C2 | semidirect |
| 143. C163 | #3156 | semidirect |
| 146. C2×#137 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104755 | 2 |
| C22×#14579689 | 2 |
| #23782239 | 2 |
| #23782236 | 2 |
| #23782058 | 2 |
| #23782056 | 2 |
| #23782046 | 2 |
| #23782043 | 2 |
| #23781623 | 2 |
| C2×#137×C163 | 2 |
| #3156 | 163 |