Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782394 | C2 | semidirect |
| 3. #23782028 | C2 | semidirect |
| 4. #23782011 | C2 | semidirect |
| 5. #23781963 | C2 | semidirect |
| 6. #23781946 | C2 | semidirect |
| 7. #23781863 | C2 | semidirect |
| 8. #23781792 | C2 | semidirect |
| 9. #23781766 | C2 | semidirect |
| 10. C4×#14579686 | C2 | semidirect |
| 11. #460×C163 | C2 | semidirect |
| 91. Q8×C163 | #41 | semidirect |
| 124. C163 | #3368 | semidirect |
| 133. #460 | D163 | semidirect |
| 204. Q8 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782394 | 2 |
| #23782335 | 2 |
| #23782028 | 2 |
| #23782011 | 2 |
| #23781963 | 2 |
| #23781946 | 2 |
| #23781863 | 2 |
| #23781792 | 2 |
| #23781766 | 2 |
| C4×#14579686 | 2 |
| #460×C163 | 2 |
| #3368 | 163 |