Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19104697 | C2 | semidirect |
| 3. C2×#19104655 | C2 | semidirect |
| 4. C2×#19104655 | C2 | semidirect |
| 5. #23781566 | C2 | semidirect |
| 6. #23781419 | C2 | semidirect |
| 7. #340×C163 | C2 | semidirect |
| 13. C2×D1304 | C4 | semidirect |
| 37. C2×D652 | C2×C4 | semidirect |
| 59. C2×C8×C163 | C2×C4 | semidirect |
| 85. D652 | C22⋊C4 | semidirect |
| 91. C2×Dic163 | D8 | semidirect |
| 146. C163 | #1879 | semidirect |
| 153. #340 | D163 | semidirect |
| 201. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| C2×#19104697 | 2 |
| C2×#19104655 | 2 |
| #23781566 | 2 |
| #23781419 | 2 |
| #340×C163 | 2 |
| #1879 | 163 |