Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23781972 | C2 | semidirect |
| 3. #23781972 | C2 | semidirect |
| 4. #23781960 | C2 | semidirect |
| 5. #23781950 | C2 | semidirect |
| 59. C2×Q8×C163 | Q8 | semidirect |
| 116. C163 | #3082 | semidirect |
| 161. C2×Q8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23781972 | 2 |
| #23781960 | 2 |
| #23781950 | 2 |
| #23781708 | 2 |
| #23781701 | 2 |
| #23781692 | 2 |
| #23781674 | 2 |
| C2×#19104659 | 2 |
| #519×C163 | 2 |
| #3082 | 163 |