Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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×#19104735 | C2 | semidirect |
| 4. #23781586 | C2 | semidirect |
| 5. #23781571 | C2 | semidirect |
| 48. C22⋊C4×C163 | Q8 | semidirect |
| 73. C2×C4×C163 | C2×Q8 | semidirect |
| 77. C22×C163 | C4⋊Q8 | semidirect |
| 93. C163 | #2434 | semidirect |
| 142. C22⋊C4 | Dic326 | semidirect |
| 167. C2×C4 | C2×Dic326 | semidirect |
| 171. C22 | #19104735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic326 | 2 |
| C2×#19104735 | 2 |
| C2×#19104714 | 2 |
| #23781586 | 2 |
| #23781571 | 2 |
| #23781540 | 2 |
| C4×C22⋊C4×C163 | 2 |
| #2434 | 163 |