Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19104768 | C2 | semidirect |
| 3. C2×#19104723 | C2 | semidirect |
| 4. C2×#19104663 | C2 | semidirect |
| 5. #23781673 | C2 | semidirect |
| 6. C2×#19104651 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 40. C2×Dic326 | D4 | semidirect |
| 62. M16×C163 | D4 | semidirect |
| 68. C42×C163 | D4 | semidirect |
| 131. C163 | #2004 | semidirect |
| 139. #339 | D163 | semidirect |
| 191. M16 | D652 | semidirect |
| 200. C42 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| #23782234 | 2 |
| C2×#19104723 | 2 |
| C2×#19104663 | 2 |
| #23781673 | 2 |
| C2×#19104651 | 2 |
| #339×C163 | 2 |
| #2004 | 163 |