Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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. C22⋊C8×D163 | C2 | semidirect |
| 3. #23781390 | C2 | semidirect |
| 4. #23781389 | C2 | semidirect |
| 5. #323×C163 | C2 | semidirect |
| 22. C2×C22⋊D163 | C8 | semidirect |
| 58. C2×Dic163 | C2×C8 | semidirect |
| 66. C23×C163 | C2×C8 | semidirect |
| 101. C163 | #1459 | semidirect |
| 107. #323 | D163 | semidirect |
| 154. C23 | C8×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C22⋊D163)⋊C4 | 2 |
| C22⋊C8×D163 | 2 |
| #23781390 | 2 |
| #23781389 | 2 |
| #323×C163 | 2 |
| #1459 | 163 |