Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
644 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 1. C2×#19104735 | C2 | semidirect |
| 3. #23781571 | C2 | semidirect |
| 4. #23781563 | C2 | semidirect |
| 5. #23781535 | C2 | semidirect |
| 39. C22×C4×C163 | Q8 | semidirect |
| 77. C22×C163 | C4⋊Q8 | semidirect |
| 86. C4×C163 | C22⋊Q8 | semidirect |
| 95. C163 | #2857 | semidirect |
| 130. C22×C4 | Dic326 | semidirect |
| 173. C22 | #19104735 | semidirect |
| 184. C4 | #19104714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104735 | 2 |
| C2×#19104714 | 2 |
| #23781571 | 2 |
| #23781563 | 2 |
| #23781535 | 2 |
| #23781525 | 2 |
| C22×C42×C163 | 2 |
| #2857 | 163 |