Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19104734 | C2 | semidirect |
| 3. #23782026 | C2 | semidirect |
| 4. #23782023 | C2 | semidirect |
| 5. #23782014 | C2 | semidirect |
| 6. #23782010 | C2 | semidirect |
| 7. #23781667 | C2 | semidirect |
| 8. #23781666 | C2 | semidirect |
| 9. #23781664 | C2 | semidirect |
| 10. M16×Dic163 | C2 | semidirect |
| 11. #417×C163 | C2 | semidirect |
| 149. C163 | #3141 | semidirect |
| 160. #417 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782211 | 2 |
| C2×#19104734 | 2 |
| #23782026 | 2 |
| #23782023 | 2 |
| #23782014 | 2 |
| #23782010 | 2 |
| #23781667 | 2 |
| #23781666 | 2 |
| #23781664 | 2 |
| M16×Dic163 | 2 |
| #417×C163 | 2 |
| #3141 | 163 |