Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19104654 | C2 | semidirect |
| 4. #23781430 | C2 | semidirect |
| 5. C22×Q16×C163 | C2 | semidirect |
| 79. C163 | #2020 | semidirect |
| 82. C22×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C2×#19104654 | 2 |
| #23781631 | 2 |
| #23781430 | 2 |
| C22×Q16×C163 | 2 |
| #2020 | 163 |