Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic326 | C2 | semidirect |
| 3. #23782016 | C2 | semidirect |
| 4. #23781996 | C2 | semidirect |
| 5. #23781951 | C2 | semidirect |
| 6. #23781894 | C2 | semidirect |
| 7. #23781871 | C2 | semidirect |
| 8. #23781806 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 11. C8×D4×C163 | C2 | semidirect |
| 83. Dic326 | #41 | semidirect |
| 96. D4×C163 | SD16 | semidirect |
| 128. C163 | #3298 | semidirect |
| 139. C8×D4 | D163 | semidirect |
| 217. D4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic326 | 2 |
| #23782319 | 2 |
| #23782016 | 2 |
| #23781996 | 2 |
| #23781951 | 2 |
| #23781894 | 2 |
| #23781871 | 2 |
| #23781806 | 2 |
| C4×#14579688 | 2 |
| C2×#19104660 | 2 |
| C8×D4×C163 | 2 |
| #3298 | 163 |