Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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×D652 | C2 | semidirect |
| 3. #23782017 | C2 | semidirect |
| 4. #23781997 | C2 | semidirect |
| 5. #23781895 | C2 | semidirect |
| 6. #23781871 | C2 | semidirect |
| 7. #23781805 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #103×D163 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 85. D652 | SD16 | semidirect |
| 98. Q8×C163 | #41 | semidirect |
| 128. C163 | #3298 | semidirect |
| 134. #475 | D163 | semidirect |
| 213. Q8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D652 | 2 |
| #23782318 | 2 |
| #23782017 | 2 |
| #23781997 | 2 |
| #23781895 | 2 |
| #23781871 | 2 |
| #23781805 | 2 |
| C4×#14579686 | 2 |
| #23781730 | 2 |
| #103×D163 | 2 |
| #475×C163 | 2 |
| #3298 | 163 |