Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781649 | C2 | semidirect |
| 3. C2×#19104651 | C2 | semidirect |
| 4. #23781437 | C2 | semidirect |
| 5. #568×C163 | C2 | semidirect |
| 42. M16×C163 | D4 | semidirect |
| 85. C163 | #1914 | semidirect |
| 87. #568 | D163 | semidirect |
| 123. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782229 | 2 |
| #23781649 | 2 |
| C2×#19104651 | 2 |
| #23781437 | 2 |
| #568×C163 | 2 |
| #1914 | 163 |