Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. Q8×Dic326 | C2 | semidirect |
| 2. #23782011 | C2 | semidirect |
| 3. #23781955 | C2 | semidirect |
| 4. #23781862 | C2 | semidirect |
| 5. Q8×C163⋊C8 | C2 | semidirect |
| 6. C4×#14579687 | C2 | semidirect |
| 45. Dic326 | #41 | semidirect |
| 51. Q8×C163 | SD16 | semidirect |
| 76. C163 | #3362 | semidirect |
| 124. Q8 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic326 | 2 |
| #23782011 | 2 |
| #23781955 | 2 |
| #23781862 | 2 |
| Q8×C163⋊C8 | 2 |
| C4×#14579687 | 2 |
| #550×C163 | 2 |
| #3362 | 163 |