Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23782463 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781669 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781437 | C2 | semidirect |
| 7. #421×C163 | C2 | semidirect |
| 36. C2×Dic326 | D4 | semidirect |
| 43. C2×D652 | D4 | semidirect |
| 55. C2×C163⋊C8 | D4 | semidirect |
| 70. M16×C163 | D4 | semidirect |
| 142. C163 | #2008 | semidirect |
| 147. #421 | D163 | semidirect |
| 208. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| C2×#19104763 | 2 |
| #23782229 | 2 |
| #23781669 | 2 |
| #23781638 | 2 |
| #23781437 | 2 |
| #421×C163 | 2 |
| #2008 | 163 |