Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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. #23781434 | C2 | semidirect |
| 4. #23781433 | C2 | semidirect |
| 5. #343×C163 | C2 | semidirect |
| 76. C163 | #1822 | semidirect |
| 82. #343 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104693 | 2 |
| #23781628 | 2 |
| #23781434 | 2 |
| #23781433 | 2 |
| #343×C163 | 2 |
| #1822 | 163 |