Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic326 | C2 | semidirect |
| 3. #23781570 | C2 | semidirect |
| 5. #23781553 | C2 | semidirect |
| 6. #23781538 | C2 | semidirect |
| 7. #23781534 | C2 | semidirect |
| 8. #23781511 | C2 | semidirect |
| 11. #19104722 | C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 41. C22⋊Dic163 | C2×C4 | semidirect |
| 44. C4×Dic163 | C2×C4 | semidirect |
| 111. C163 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104722 | 2 |
| C2×C4×Dic326 | 2 |
| #23781570 | 2 |
| #23781568 | 2 |
| #23781553 | 2 |
| #23781538 | 2 |
| #23781534 | 2 |
| #23781511 | 2 |
| C2×C4×D4×C163 | 2 |
| #2326 | 163 |