Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23781842 | C2 | direct (N × H) |
| 4. C2×#19104663 | C2 | semidirect |
| 5. C2×#19104652 | C2 | semidirect |
| 6. C2×#124×C163 | C2 | semidirect |
| 15. #19104766 | C22 | semidirect |
| 18. C2×#14579683 | C22 | semidirect |
| 19. #19104663 | C22 | semidirect |
| 20. #19104652 | C22 | semidirect |
| 21. C22×Q8×C163 | C22 | semidirect |
| 24. #124×C163 | C22 | semidirect |
| 26. C2×C42×C163 | C22 | semidirect |
| 47. #14579683 | C23 | semidirect |
| 53. C2×Q8×C163 | C23 | semidirect |
| 63. C42×C163 | C23 | semidirect |
| 116. C2×C163 | #455 | semidirect |
| 119. C163 | C2×#455 | semidirect |
| 123. C2×#124 | D163 | semidirect |
| 132. C22×Q8 | C2×D163 | semidirect |
| 142. #124 | C2×D163 | semidirect |
| 144. C2×C42 | C2×D163 | semidirect |
| 159. C2×Q8 | C22×D163 | semidirect |
| 183. C42 | C22×D163 | semidirect |
| 237. C2 | #23781842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104766 | 2 |
| #23781842 | 2 |
| C2×#19104663 | 2 |
| C2×#19104652 | 2 |
| C2×#124×C163 | 2 |
| C2×#455 | 163 |