Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#19104692 | C2 | semidirect |
| 3. C2×C4⋊C4×D163 | C2 | semidirect |
| 4. #23781571 | C2 | semidirect |
| 5. #23781570 | C2 | semidirect |
| 6. #23781568 | C2 | semidirect |
| 7. #23781541 | C2 | semidirect |
| 8. #23781523 | C2 | semidirect |
| 9. #390×C163 | C2 | semidirect |
| 12. C2×#14579698 | C4 | semidirect |
| 36. C2×Dic326 | C2×C4 | semidirect |
| 42. C22×Dic163 | C2×C4 | semidirect |
| 61. C2×D4×C163 | C2×C4 | semidirect |
| 88. C4×D163 | C22⋊C4 | semidirect |
| 133. C163 | #2311 | semidirect |
| 141. #390 | D163 | semidirect |
| 177. C2×D4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104692 | 2 |
| C2×C4⋊C4×D163 | 2 |
| #23781571 | 2 |
| #23781570 | 2 |
| #23781568 | 2 |
| #23781541 | 2 |
| #23781523 | 2 |
| #390×C163 | 2 |
| #2311 | 163 |