Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23782465 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. #23782234 | C2 | semidirect |
| 4. #23781681 | C2 | semidirect |
| 5. #23781671 | C2 | semidirect |
| 6. #23781638 | C2 | semidirect |
| 7. #344×C163 | C2 | semidirect |
| 41. C2×Dic326 | D4 | semidirect |
| 50. C2×D652 | D4 | semidirect |
| 69. M16×C163 | D4 | semidirect |
| 71. C2×C8×C163 | D4 | semidirect |
| 142. C163 | #2008 | semidirect |
| 150. #344 | D163 | semidirect |
| 208. M16 | D652 | semidirect |
| 210. C2×C8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| C2×#19104763 | 2 |
| #23782234 | 2 |
| #23781681 | 2 |
| #23781671 | 2 |
| #23781638 | 2 |
| #344×C163 | 2 |
| #2008 | 163 |