Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14579682 | C2 | semidirect |
| 2. C2×#19104706 | C2 | semidirect |
| 3. #23781915 | C2 | direct (N × H) |
| 4. C2×#19104667 | C2 | semidirect |
| 5. C2×#19104656 | C2 | semidirect |
| 6. C22×D8×C163 | C2 | semidirect |
| 10. C2×#14579682 | C22 | semidirect |
| 13. #19104706 | C22 | semidirect |
| 16. #19104667 | C22 | semidirect |
| 17. #19104656 | C22 | semidirect |
| 20. C2×D8×C163 | C22 | semidirect |
| 44. C2×C8×C163 | D4 | semidirect |
| 70. C8×C163 | C2×D4 | semidirect |
| 87. C2×C163 | #469 | semidirect |
| 91. C163 | C2×#469 | semidirect |
| 93. C22×D8 | D163 | semidirect |
| 103. C2×D8 | C2×D163 | semidirect |
| 133. C2×C8 | C22⋊D163 | semidirect |
| 162. C8 | C2×C22⋊D163 | semidirect |
| 180. C2 | #23781915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579682 | 2 |
| C2×#19104706 | 2 |
| #23781915 | 2 |
| C2×#19104667 | 2 |
| C2×#19104656 | 2 |
| C22×D8×C163 | 2 |
| C2×#469 | 163 |