Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #23781703 | C2 | direct (N × H) |
| 3. C2×#19104669 | C2 | semidirect |
| 4. C2×#19104667 | C2 | semidirect |
| 11. #19104669 | C22 | semidirect |
| 12. #19104667 | C22 | semidirect |
| 14. C22×C8×C163 | C4 | semidirect |
| 32. C2×C8×C163 | C2×C4 | semidirect |
| 64. C2×C163 | #427 | semidirect |
| 67. C163 | C2×#427 | semidirect |
| 75. C22×C8 | Dic163 | semidirect |
| 96. C2×C8 | C2×Dic163 | semidirect |
| 132. C2 | #23781703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104694 | 2 |
| #23781703 | 2 |
| C2×#19104669 | 2 |
| C2×#19104667 | 2 |
| C23×C8×C163 | 2 |
| C2×#427 | 163 |