Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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×#19104700 | C2 | semidirect |
| 3. #23781566 | C2 | semidirect |
| 4. #23781565 | C2 | semidirect |
| 5. #23781524 | C2 | semidirect |
| 6. C4×C22⋊Dic163 | C2 | semidirect |
| 7. #23781512 | C2 | semidirect |
| 8. #380×C163 | C2 | semidirect |
| 10. C2×#14579699 | C4 | semidirect |
| 60. Dic326 | C22⋊C4 | semidirect |
| 70. C2×Dic163 | #41 | semidirect |
| 114. C163 | #2341 | semidirect |
| 121. #380 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104700 | 2 |
| #23781566 | 2 |
| #23781565 | 2 |
| #23781524 | 2 |
| C4×C22⋊Dic163 | 2 |
| #23781512 | 2 |
| #380×C163 | 2 |
| #2341 | 163 |