Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14579689 | C2 | semidirect |
| 3. #23782044 | C2 | semidirect |
| 4. #23781904 | C2 | semidirect |
| 5. #23781875 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 7. #23781821 | C2 | semidirect |
| 8. #23781820 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 52. #14579689 | D4 | direct (N × H) |
| 100. D4×C163 | Q16 | semidirect |
| 113. C22×C163 | C2×Q16 | semidirect |
| 120. C4×C163 | C2×Q16 | semidirect |
| 130. C163 | D4×Q16 | semidirect |
| 224. D4 | #14579689 | direct (N × H) |
| 244. C22 | C2×#14579689 | semidirect |
| 254. C4 | C2×#14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| D4×Dic326 | 2 |
| #23782044 | 2 |
| #23781904 | 2 |
| #23781875 | 2 |
| #23781872 | 2 |
| #23781821 | 2 |
| #23781820 | 2 |
| C4×#14579689 | 2 |
| D4×C163⋊C8 | 2 |
| D4×Q8×C163 | 2 |
| D4×Q16 | 163 |