Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #23781523 | C2 | semidirect |
| 4. #23781432 | C2 | semidirect |
| 5. #342×C163 | C2 | semidirect |
| 8. C22×C4×D163 | C4 | semidirect |
| 12. C2×Dic163⋊C4 | C4 | semidirect |
| 14. C2×(C2×D163)⋊C4 | C4 | semidirect |
| 15. C2×C4×Dic163 | C4 | semidirect |
| 53. C22×D163 | C4⋊C4 | semidirect |
| 68. C2×Dic163 | C4⋊C4 | semidirect |
| 109. Dic163 | #99 | semidirect |
| 118. C163 | #1799 | semidirect |
| 124. #342 | 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 |
| C2×#19104649 | 2 |
| #23781523 | 2 |
| #23781432 | 2 |
| #342×C163 | 2 |
| #1799 | 163 |