Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#19104766 | C2 | semidirect |
| 3. #23781847 | C2 | semidirect |
| 4. #23781842 | C2 | semidirect |
| 5. #23781683 | C2 | semidirect |
| 6. #23781649 | C2 | semidirect |
| 7. #536×C163 | C2 | semidirect |
| 17. #19104766 | C22 | semidirect |
| 20. C2×#14579683 | C22 | semidirect |
| 21. #19104663 | C22 | semidirect |
| 22. #19104654 | C22 | semidirect |
| 23. #19104652 | C22 | semidirect |
| 25. C22×Q8×C163 | C22 | semidirect |
| 26. C4⋊Q8×C163 | C22 | semidirect |
| 27. #124×C163 | C22 | semidirect |
| 30. #117×C163 | C22 | semidirect |
| 129. C163 | #3022 | semidirect |
| 133. #536 | D163 | semidirect |
| 147. C22×Q8 | C2×D163 | semidirect |
| 153. C4⋊Q8 | C2×D163 | semidirect |
| 154. #124 | C2×D163 | semidirect |
| 157. #117 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104766 | 2 |
| #23781847 | 2 |
| #23781842 | 2 |
| #23781683 | 2 |
| #23781649 | 2 |
| #536×C163 | 2 |
| #3022 | 163 |