Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C22⋊C4×D163 | C2 | semidirect |
| 3. C2×#19104649 | C2 | semidirect |
| 4. C2×#19104649 | C2 | semidirect |
| 5. #23781520 | C2 | semidirect |
| 6. #23781432 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 9. C22×D652 | C4 | semidirect |
| 19. C2×(C2×D163)⋊C4 | C4 | semidirect |
| 33. C23×D163 | C2×C4 | semidirect |
| 48. C22×Dic163 | C2×C4 | semidirect |
| 54. C22⋊Dic163 | D4 | semidirect |
| 62. C22×C4×C163 | C2×C4 | semidirect |
| 68. C22⋊C4×C163 | D4 | semidirect |
| 152. C2×D163 | #99 | semidirect |
| 170. C163 | #1898 | semidirect |
| 178. #342 | D163 | semidirect |
| 225. C22×C4 | C4×D163 | semidirect |
| 239. C22⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104705 | 2 |
| C2×C22⋊C4×D163 | 2 |
| C2×#19104649 | 2 |
| #23781520 | 2 |
| #23781432 | 2 |
| #342×C163 | 2 |
| #1898 | 163 |