Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 197 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. #23781547 | C2 | semidirect |
| 4. C4×Dic163⋊C4 | C2 | semidirect |
| 6. C42×Dic163 | C2 | semidirect |
| 7. #376×C163 | C2 | semidirect |
| 9. #19104692 | C4 | semidirect |
| 75. C163 | #2298 | semidirect |
| 82. #376 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104692 | 2 |
| #23781554 | 2 |
| #23781547 | 2 |
| C4×Dic163⋊C4 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C42×Dic163 | 2 |
| #376×C163 | 2 |
| #2298 | 163 |