Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic326 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23782010 | C2 | semidirect |
| 5. #23781955 | C2 | semidirect |
| 6. #23781954 | C2 | semidirect |
| 7. #23781865 | C2 | semidirect |
| 8. #23781863 | C2 | semidirect |
| 9. C8×Dic326 | C2 | semidirect |
| 10. #23781750 | C2 | semidirect |
| 11. C4×SD16×C163 | C2 | semidirect |
| 77. Dic326 | SD16 | semidirect |
| 91. Q8×C163 | #41 | semidirect |
| 125. C163 | #3362 | semidirect |
| 137. C4×SD16 | D163 | semidirect |
| 206. Q8 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic326 | 2 |
| #23782336 | 2 |
| #23782012 | 2 |
| #23782010 | 2 |
| #23781955 | 2 |
| #23781954 | 2 |
| #23781865 | 2 |
| #23781863 | 2 |
| C8×Dic326 | 2 |
| #23781750 | 2 |
| C4×SD16×C163 | 2 |
| #3362 | 163 |