Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782035 | C2 | semidirect |
| 4. #23782034 | C2 | semidirect |
| 5. #23782033 | C2 | semidirect |
| 6. #23782014 | C2 | semidirect |
| 9. #491×C163 | C2 | semidirect |
| 87. C163 | #3139 | semidirect |
| 94. #491 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782221 | 2 |
| C4⋊Q8×D163 | 2 |
| #23782035 | 2 |
| #23782034 | 2 |
| #23782033 | 2 |
| #23782014 | 2 |
| #23781672 | 2 |
| #23781617 | 2 |
| #491×C163 | 2 |
| #3139 | 163 |